The Cosine function ( cos (x) ) The cosine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the adjacent side to the hypotenuse. It is the complement to the sine. In the illustration below, cos (α) = b/c and cos (β) = a/c. (cotx)2 +1 = (cosecx)2 Odd and even properties cos( x) = cos(x) sin( x) = sin(x) tan( x) = tan(x) Double angle formulas sin(2x) = 2sinxcosx cos(2x) = (cosx)2 (sinx)2 cos(2x) = 2(cosx)2 1 cos(2x) = 1 2(sinx)2 Half angle formulas sin(1 2 x) 2 = 1 2 (1 cosx) cos(1 2 x) 2 = 1 2 (1+cosx) Sums and di erences of angles cos(A+B) = cosAcosB sinAsinB cos ... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Solve for x cos(x)(cos(x)-1)=0. Step 1. If any individual factor on the left side of the equation is equal to , the entire expression will be equal to . Step 2.Graph y=cos(x-1) Step 1. Use the form to find the variables used to find the amplitude, period, phase shift, ... Step 6.5.1. Replace the variable with in the expression. Solve for x cos(x)(cos(x)-1)=0. Step 1. If any individual factor on the left side of the equation is equal to , the entire expression will be equal to . Step 2.sin2x +cos2x = 1. where we can subtract cos2x from both sides to get what we have in blue above: sin2x = 1 − cos2x. Thus, this expression is equal to. sin2x. All we did was use the difference of squares property to our advantage, recognize that the expression we had is derived from the Pythagorean Identity, use it, and simplify. Hope this helps!קוסינוס (מסומן ב- ) היא פונקציה טריגונומטרית בסיסית, המתאימה לכל זווית מספר ממשי בין (1-) ל-1. הרחבות שונות של הפונקציה משמשות במגוון תחומים, כגון: הגדרות שונות ב אנליזה (ובפרט ב אנליזה מרוכבת ... We will begin by multiplying 1 cosx − 1 by the conjugate of cosx − 1, which is cosx + 1: 1 cosx − 1 ⋅ cosx + 1 cosx + 1. You may wonder why we do this. It's so we can apply the difference of squares property, (a −b)(a +b) = a2 −b2, in the denominator, to simplify it a little. Back to the problem:First of all, note that implicitly differentiating cos(cos−1x)= x does not prove the existence of the derivative of cos−1 x. What it does show, however, ... By definition we have that for x ∈ [0,2π] for 0 ≤ x≤ π cos−1 cosx = x for π< x ≤ 2π cos−1 cosx = 2π−x and this is periodic with period T = 2π. Thus it ... Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Trigonometric Identities Resources · Cool Tools · Formulas & Tables · References · Test Preparation · Study Tips · Wonders of Math Search Trigonometric Identities ( Math | Trig | Identities) sin (-x) = -sin (x) csc (-x) = -csc (x) cos (-x) = cos (x) sec (-x) = sec (x) tan (-x) = -tan (x) cot (-x) = -cot (x)Explanation: Use the identity: secx = 1 cosx. 1 secx = 1 1 cosx = 1 ⋅ cosx 1 = cosx. Answer link.From Pythagoras theorem we get: sin2x +cos2x = 1. So: sin2x = 1 − cos2x = (1 − cosx)(1 + cosx) Answer link.We would like to show you a description here but the site won’t allow us. Solve for x cos (x)=1. cos (x) = 1 cos ( x) = 1. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(1) x = arccos ( 1) Simplify the right side. Tap for more steps... x = 0 x = 0. The cosine function is positive in the first and fourth quadrants. To find the second solution, subtract the ... The area, 1 / 2 × base × height, of an isosceles triangle is calculated, first when upright, and then on its side. When upright, the area = sin θ cos θ {\displaystyle \sin \theta \cos \theta } . Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. May 4, 2018 · Explanation: since cosx < 0 then x is in second/third quadrants. x = cos−1( 1 √2) = π 4 ← related acute angle. ⇒ x = π− π 4 = 3π 4 ← second quadrant. or x = π+ π 4 = 5π 4 ← third quadrant. due to the periodicity of the cosine the solutions will. repeat every 2π. solutions are. x = 3π 4 +2nπ → (n ∈ Z) Jan 26, 2017 · Explanation: Use the identity: secx = 1 cosx. 1 secx = 1 1 cosx = 1 ⋅ cosx 1 = cosx. Answer link. May 27, 2017 · The first step is to multiply the two expressions between parentheses : (II) There is a trigonometric identity that states : Working with this expression : ⇒. (I) Using the equation (I) in (II) : ⇒. arrow right. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.May 29, 2023 · Misc 16 Find the derivative of the following functions (it is to be understood that a, b, c, d, p, q, r and s are fixed non-zero constants and m and n are integers ... Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Aug 16, 2016 · False due to a clash of conventions. If n > 1 is a positive integer, then: cos^n x = (cos x)^n This is a convenience of notation, to avoid having to use parentheses to distinguish, for example: (cos x)^2 and cos (x^2) By convention we can write: cos^2 x and cos x^2 respectively, without ambiguity. However, in the case of -1, we have a clash of notation. If f(x) is a function, then f^(-1)(x) is ... Sine and Cosine Laws in Triangles. In any triangle we have: 1 - The sine law. sin A / a = sin B / b = sin C / c. 2 - The cosine laws. a 2 = b 2 + c 2 - 2 b c cos A. b 2 = a 2 + c 2 - 2 a c cos B. c 2 = a 2 + b 2 - 2 a b cos C.Explanation: Use the identity: secx = 1 cosx. 1 secx = 1 1 cosx = 1 ⋅ cosx 1 = cosx. Answer link.Arccos. Arccosine, written as arccos or cos -1 (not to be confused with ), is the inverse cosine function. Both arccos and cos -1 are the same thing. Cosine only has an inverse on a restricted domain, 0 ≤ x ≤ π. In the figure below, the portion of the graph highlighted in red shows the portion of the graph of cos (x) that has an inverse.My origin equation is 2 x^2 (-1 + Cos[x] Cosh[x]) == 0, how could I know I should first divide the equation by x^2, before applying your code on big x approximation.What is tan 30 using the unit circle? tan 30° = 1/√3. To find this answer on the unit circle, we start by finding the sin and cos values as the y-coordinate and x-coordinate, respectively: sin 30° = 1/2 and cos 30° = √3/2. Now use the formula. Recall that tan 30° = sin 30° / cos 30° = (1/2) / (√3/2) = 1/√3, as claimed.In looking through the ways to find the limit of (1-cos(x)) / x, we looked into a couple methods. The first method is the plug-in method, which involves simply plugging a into (1-cos(x)) / x for x.We will begin by multiplying 1 cosx − 1 by the conjugate of cosx − 1, which is cosx + 1: 1 cosx − 1 ⋅ cosx + 1 cosx + 1. You may wonder why we do this. It's so we can apply the difference of squares property, (a −b)(a +b) = a2 −b2, in the denominator, to simplify it a little. Back to the problem:We would like to show you a description here but the site won’t allow us.Dec 22, 2021 · Steps to Solve Limit of 1-Cos(x)/xWhen it comes to finding the limit of a function, as x approaches some value a, there are many different methods that can be attempted.Depending on the function ... My origin equation is 2 x^2 (-1 + Cos[x] Cosh[x]) == 0, how could I know I should first divide the equation by x^2, before applying your code on big x approximation.1+cosx. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by ... Pythagorean identities Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.Feb 13, 2017 · Just as the distance between the origin and any point #(x,y)# on a circle must be the circle's radius, the sum of the squared values for #sin theta# and #cos theta# must be 1 for any angle #theta#. Answer link In mathematics, the trigonometric functions (also called circular functions, angle functions or goniometric functions [1] [2]) are real functions which relate an angle of a right-angled triangle to ratios of two side lengths.Step 1: The first thing we want to do is look at the functions in the numerator and denominator. By inspection, we see that the values for f (x) and g (x) would be 1 and tan (x), respectively ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...lim_(x->0) (cos(x)-1)/x = 0. We determine this by utilising L'hospital's Rule. To paraphrase, L'Hospital's rule states that when given a limit of the form lim_(x→a)f(x)/g(x), where f(a) and g(a) are values that cause the limit to be indeterminate (most often, if both are 0, or some form of ∞), then as long as both functions are continuous and differentiable at and in the vicinity of a, one ...Multiply by 1 + cosx 1 + cosx to get. 1 − cos2x x(1 + cosx) = sin2x x(1 +cosx) = sinx ⋅ sinx x ⋅ 1 1 + cosx. Taking the limit as x → 0 gives. (0)(1)(1 2) = 0. Answer link.First of all, note that implicitly differentiating cos(cos−1x)= x does not prove the existence of the derivative of cos−1 x. What it does show, however, ... By definition we have that for x ∈ [0,2π] for 0 ≤ x≤ π cos−1 cosx = x for π< x ≤ 2π cos−1 cosx = 2π−x and this is periodic with period T = 2π. Thus it ...Graph y=cos(x-1) Step 1. Use the form to find the variables used to find the amplitude, period, phase shift, and vertical shift. Step 2. Find the amplitude . Amplitude:Precalculus. Simplify (1-cos (x))/ (cos (x)) Step 1. Nothing further can be done with this topic. Please check the expression entered or try another topic. Jan 31, 2017 · 1. Hint The appearance of 1 + cos x 1 + cos x suggests we can produce an expression without a constant term in the denominator by substituting x = 2t x = 2 t and using the half-angle identity cos2 t = 12(1 + cos 2t) cos 2 t = 1 2 ( 1 + cos 2 t). Share. Method 2: Note that: $$ \int_{y=0}^\infty e^{-(x^2+4)y}\,dy=\frac{1}{x^2+4}, $$ therefore $$ \int_{x=0}^\infty\int_{y=0}^\infty e^{-(x^2+4)y}\cos2x\,dy\,dx=\int_0 ...Write each expression with a common denominator of (1−cos(x))(1+ cos(x)) ( 1 - cos ( x)) ( 1 + cos ( x)), by multiplying each by an appropriate factor of 1 1. Tap for more steps... Combine the numerators over the common denominator. Simplify the numerator.Use the identity: cos (a + b) = cos a.cos b - sin a.sin b cos 2x = cos (x + x) = cos x.cos x - sin x. sin x = cos^2 x - sin^2 x = = cos^2 x - (1 - cos^2 x) = 2cos ^2 ...Simplify cos(x)*cos(x) Step 1. Raise to the power of . Step 2. Raise to the power of . Step 3. Use the power rule to combine exponents. Step 4. Add and . E 1 (sin x, cos x, tan x) = E 2 (sin x, cos x, tan x) Where E 1 and E 2 are rational functions. Since sine, cosine and tangent are the major trigonometric functions, hence the solutions will be derived for the equations comprising these three ratios. However, the solutions for the other three ratios such as secant, cosecant and cotangent can be ... The equation is. cosx − 1 = − cosx. ⇒, 2cosx = 1. ⇒, cosx = 1 2. The solutions are. {x = π 3 + 2kπ x = 5 3π +2kπ, ∀k ∈ Z. Answer link.cos( ) = x 1 = x sec( ) = 1 x tan( ) = y x cot( ) = x y FactsandProperties Domain Thedomainisallthevaluesof thatcanbe pluggedintothefunction. sin( ), canbeanyangleVDOM DHTML tml>. What is 1+cosx=? - Quora. Something went wrong. Wait a moment and try again.So I've been trying to show that $ | \cos x - 1 | \leq | x | $ for all x values, usin... Stack Exchange Network Stack Exchange network consists of 183 Q&A communities including Stack Overflow , the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.Solve for ? cos (x)=1/2. cos (x) = 1 2 cos ( x) = 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(1 2) x = arccos ( 1 2) Simplify the right side. Tap for more steps... x = π 3 x = π 3. The cosine function is positive in the first and fourth quadrants. E 1 (sin x, cos x, tan x) = E 2 (sin x, cos x, tan x) Where E 1 and E 2 are rational functions. Since sine, cosine and tangent are the major trigonometric functions, hence the solutions will be derived for the equations comprising these three ratios. However, the solutions for the other three ratios such as secant, cosecant and cotangent can be ...Precalculus. Simplify (1-cos (x))/ (cos (x)) Step 1. Nothing further can be done with this topic. Please check the expression entered or try another topic. Ex 7.3, 8 1 − 𝑐𝑜𝑠 𝑥1 + 𝑐𝑜𝑠 𝑥 1 − cos𝑥1 + cos𝑥 We know that Thus, our equation becomes 1 − cos𝑥1 + cos𝑥 𝑑𝑥= 2 sin2 𝑥22 cos2 𝑥2 = sin2 𝑥2 cos2 𝑥2 𝑑𝑥 = tan2 ...VDOM DHTML tml>. What is the formula of 1+cosx? - Quora. Something went wrong.Free trigonometric equation calculator - solve trigonometric equations step-by-step The first step is to multiply the two expressions between parentheses : (II) There is a trigonometric identity that states : Working with this expression : ⇒. (I) Using the equation (I) in (II) : ⇒. arrow right.Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...קוסינוס (מסומן ב- ) היא פונקציה טריגונומטרית בסיסית, המתאימה לכל זווית מספר ממשי בין (1-) ל-1. הרחבות שונות של הפונקציה משמשות במגוון תחומים, כגון: הגדרות שונות ב אנליזה (ובפרט ב אנליזה מרוכבת ...Free trigonometric equation calculator - solve trigonometric equations step-by-stepOct 3, 2016 · Multiply by 1 + cosx 1 + cosx to get. 1 − cos2x x(1 + cosx) = sin2x x(1 +cosx) = sinx ⋅ sinx x ⋅ 1 1 + cosx. Taking the limit as x → 0 gives. (0)(1)(1 2) = 0. Answer link. From Pythagoras theorem we get: sin2x +cos2x = 1. So: sin2x = 1 − cos2x = (1 − cosx)(1 + cosx) Answer link.Precalculus. Solve for ? cos (x)=1/3. cos (x) = 1 3 cos ( x) = 1 3. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(1 3) x = arccos ( 1 3) Simplify the right side. Tap for more steps... x = 1.23095941 x = 1.23095941. The cosine function is positive in the first and fourth quadrants.sec A = 1/cos A tan A = sin A/cos A sin^2 A + cos^2 A = 1 sec x + tan x = (1+sin x)/cos x = ((1+sin x)(1-sin x))/(cos x(1-sin x)) = (1-sin^2 x)/(cos x(1-sin x)) = cos ...Method 2: Note that: $$ \int_{y=0}^\infty e^{-(x^2+4)y}\,dy=\frac{1}{x^2+4}, $$ therefore $$ \int_{x=0}^\infty\int_{y=0}^\infty e^{-(x^2+4)y}\cos2x\,dy\,dx=\int_0 ...Just as the distance between the origin and any point #(x,y)# on a circle must be the circle's radius, the sum of the squared values for #sin theta# and #cos theta# must be 1 for any angle #theta#. Answer linkCompute answers using Wolfram's breakthrough technology & knowledgebase, relied on by millions of students & professionals. For math, science, nutrition, history ...Explanation: since cosx < 0 then x is in second/third quadrants. x = cos−1( 1 √2) = π 4 ← related acute angle. ⇒ x = π− π 4 = 3π 4 ← second quadrant. or x = π+ π 4 = 5π 4 ← third quadrant. due to the periodicity of the cosine the solutions will. repeat every 2π. solutions are. x = 3π 4 +2nπ → (n ∈ Z)Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor. Trigonometry. Solve for ? cos (x)=-1/2. cos (x) = − 1 2 cos ( x) = - 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(−1 2) x = arccos ( - 1 2) Simplify the right side. Tap for more steps... x = 2π 3 x = 2 π 3. The cosine function is negative in the second and third quadrants.Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.Jun 24, 2016 · This can be done by the useful technique of differentiating under the integral sign. In fact, this is exercise 10.23 in the second edition of "Mathematical Analysis" by Tom Apostol. Pythagorean identities Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.Dec 22, 2021 · Steps to Solve Limit of 1-Cos(x)/xWhen it comes to finding the limit of a function, as x approaches some value a, there are many different methods that can be attempted.Depending on the function ... Hero and Nghi, I think I could invoke more interest by including the. solutions for cosx − sinx = 1, and for that matter, secx ± tanx = 1, that become. cosx − sinx = 1 and cosx +sinx = 1, upon multiplication by. cos x, when x ≠ an odd multiple of π 2. For cos x - sin x = 1, the general solution is. x = 2nπ and x = (4n − 1) π 2,n = 0 ...Found 2 solutions by josgarithmetic, Boreal: Answer by josgarithmetic (38702) ( Show Source ): You can put this solution on YOUR website! Answer by Boreal (15207) ( Show Source ): You can put this solution on YOUR website! cosx/ (1+sinx) cos x (1-sinx)/ [ (1+sinx) (1-sinx)] ;; multiply by (1-sin x/1-sin x) cosx-sinxcosx/ (1-sin^2x) ;;; 1-sin^2x ... Jul 24, 2018 · The equation is. cosx − 1 = − cosx. ⇒, 2cosx = 1. ⇒, cosx = 1 2. The solutions are. {x = π 3 + 2kπ x = 5 3π +2kπ, ∀k ∈ Z. Answer link. Mathematically, it is written as cos-1 (x) and is the inverse function of the trigonometric function cosine, cos(x). An important thing to note is that inverse cosine is not the reciprocal of cos x. There are 6 inverse trigonometric functions as sin-1 x, cos-1 x, tan-1 x, csc-1 x, sec-1 x, cot-1 x.Solve for x cos(x)(cos(x)-1)=0. Step 1. If any individual factor on the left side of the equation is equal to , the entire expression will be equal to . Step 2.(cotx)2 +1 = (cosecx)2 Odd and even properties cos( x) = cos(x) sin( x) = sin(x) tan( x) = tan(x) Double angle formulas sin(2x) = 2sinxcosx cos(2x) = (cosx)2 (sinx)2 cos(2x) = 2(cosx)2 1 cos(2x) = 1 2(sinx)2 Half angle formulas sin(1 2 x) 2 = 1 2 (1 cosx) cos(1 2 x) 2 = 1 2 (1+cosx) Sums and di erences of angles cos(A+B) = cosAcosB sinAsinB cos ...sec A = 1/cos A tan A = sin A/cos A sin^2 A + cos^2 A = 1 sec x + tan x = (1+sin x)/cos x = ((1+sin x)(1-sin x))/(cos x(1-sin x)) = (1-sin^2 x)/(cos x(1-sin x)) = cos ...
Trigonometry. Solve for ? cos (x)=-1/2. cos (x) = − 1 2 cos ( x) = - 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(−1 2) x = arccos ( - 1 2) Simplify the right side. Tap for more steps... x = 2π 3 x = 2 π 3. The cosine function is negative in the second and third quadrants.. Harrington
Period of a solution in a trigonometric equation https://math.stackexchange.com/questions/1297742/period-of-a-solution-in-a-trigonometric-equation sin and cos have period 2π and tan has period π. When solving an equation, make sure to list all roots in a period. tanx =0 x = 0 in [0,π), i.e. x = kπ. tanx = 1 x= 4π ...1+cosx. Natural Language; Math Input; Extended Keyboard Examples Upload Random. Compute answers using Wolfram's breakthrough technology & knowledgebase, relied on by ... The Cosine function ( cos (x) ) The cosine is a trigonometric function of an angle, usually defined for acute angles within a right-angled triangle as the ratio of the length of the adjacent side to the hypotenuse. It is the complement to the sine. In the illustration below, cos (α) = b/c and cos (β) = a/c. Free math problem solver answers your algebra, geometry, trigonometry, calculus, and statistics homework questions with step-by-step explanations, just like a math tutor.May 27, 2017 · The first step is to multiply the two expressions between parentheses : (II) There is a trigonometric identity that states : Working with this expression : ⇒. (I) Using the equation (I) in (II) : ⇒. arrow right. The fixed point iteration x n+1 = cos(x n) with initial value x 0 = −1 converges to the Dottie number. Zero is the only real fixed point of the sine function; in other words the only intersection of the sine function and the identity function is sin ( 0 ) = 0 {\displaystyle \sin(0)=0} . It follows that. arccos(cos x) = arccos(cos(d(x))) = d(x) (x ∈ R) , arccos ( cos x) = arccos ( cos ( d ( x))) = d ( x) ( x ∈ R) , which reveals arccos ∘ cos arccos ∘ cos to be a sawtooth function. Share. edited Aug 29, 2018 at 1:58. user46234. answered Mar 10, 2018 at 17:31. Christian Blatter.Step 1: The first thing we want to do is look at the functions in the numerator and denominator. By inspection, we see that the values for f (x) and g (x) would be 1 and tan (x), respectively ...We will begin by multiplying 1 cosx − 1 by the conjugate of cosx − 1, which is cosx + 1: 1 cosx − 1 ⋅ cosx + 1 cosx + 1. You may wonder why we do this. It's so we can apply the difference of squares property, (a −b)(a +b) = a2 −b2, in the denominator, to simplify it a little. Back to the problem:Free trigonometric equation calculator - solve trigonometric equations step-by-stepE 1 (sin x, cos x, tan x) = E 2 (sin x, cos x, tan x) Where E 1 and E 2 are rational functions. Since sine, cosine and tangent are the major trigonometric functions, hence the solutions will be derived for the equations comprising these three ratios. However, the solutions for the other three ratios such as secant, cosecant and cotangent can be ...קוסינוס (מסומן ב- ) היא פונקציה טריגונומטרית בסיסית, המתאימה לכל זווית מספר ממשי בין (1-) ל-1. הרחבות שונות של הפונקציה משמשות במגוון תחומים, כגון: הגדרות שונות ב אנליזה (ובפרט ב אנליזה מרוכבת ...Pythagorean identities Trigonometric functions and their reciprocals on the unit circle. All of the right-angled triangles are similar, i.e. the ratios between their corresponding sides are the same. For sin, cos and tan the unit-length radius forms the hypotenuse of the triangle that defines them.Trigonometry. Solve for ? cos (x)=-1/2. cos (x) = − 1 2 cos ( x) = - 1 2. Take the inverse cosine of both sides of the equation to extract x x from inside the cosine. x = arccos(−1 2) x = arccos ( - 1 2) Simplify the right side. Tap for more steps... x = 2π 3 x = 2 π 3. The cosine function is negative in the second and third quadrants..