3. When e is in standard position and its terminal side passes through the point (4, -2) Find the exact value of cose.

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A: Please refer to the image below

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Q: **#1.) In triangle JKL, mZK = 90° and tanl = Determine the value of cos). %3D

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A: Given: Line y=-2x in quadrant II. Note: 1] sinu is positive in quadrant II 2] cosu is negative in…

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A: In the question we have to find the angle of cosine which is lying in third quadrant as cosine is…

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Q: (-1) cos[cosh (In ")]dr 4.

A:

Q: To four decimal places , find all solutions for Cos X = 8.

A: To find the solution of the given trigonometric equation.

Q: Find the solutions of the equation that are in the interval [0, 2π).

A: the given equation is: sin2u=sinu we have to find the solutions of the given equation in the…

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A: A delta function is defined as δ(t-a)=0     for t≠a∞   for t=a. The fundamental property of the…

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A: We have to solve Integral

Q: 12 "2 If Y= \n(Sinae), Prove y =y=- ノ

A: Here, the given function is: y=ln(sin x) So, y'=1sin x(cos x)=tanxy''=ddx(y')=ddx(tan x)=sec2x

Q: 4) state laylors your estima te 5) Using in Taylor's Theorem, show that the error in 3) for cos…

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Q: Find the Integrationof {(u) = tanu + Cos 24. %3D

A: Consider the function, fu=tanu2+cos2u

Q: Solve che DE'sin with Euler 2?

A: For the solution follow the next steps.

Q: 3. Show that the equation 1 + cos(x) – 2sin(=) = 0 has a solution in the interval [0, 7 /2].

A:

Q: TO 2 8. х cOs 2x dx

A: We have to calculate the given integral   The given integral is

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Q: 2. What is the exact value of cos()? |(0, 1) (글,

A: Graph is symmetrical in -2 to 2. So the midline of function is y=0.

Q: If cos A %3D with A in QII V10 Find tan 2A. HIN

A:

Q: Find all solutions of the equation in the interval [0. 2x). 3 tan e %3D

A: tanθ=32 θ=tan-1(32) θ=0.983   as the solution lies in [0,2π)   possible values of θ = 0.983+kπ where…

Q: Im Sin (n-y) Cos (+9)

A: We find limit of given function

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Q: Show that the equation has exactly one real root. 2x + cos(x) = 0 %3D

A: Our Aim is to show that the equation 2x+cos (x)=0 has exactly onereal root.

Q: I co cos (In x) dr

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Q: In cof '3x sinAte ech x² 2

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Q: Show that the equation 2x + cos(x) = 1 has exactly one root. (IVT and Rolle's Theorem)

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Q: Find all exact solutions on [0,2x) of the equation cos 2t = sint +1

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Q: Express (cos(40) + i sin(28))² in exponential form

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Q: ☺ Find tue indefinile intgrel. cos (5@] do

A: ∫un du = un+1n+1+C ; where, 'C' is an integration constant.

Q: Find the exact value of the expression. TC COS 16 3T - sin 16 TO - sin 16 COS | 16

A: To find:- Exact value of cosπ16cos3π16-cosπ16cos3π16

Q: 35. Use property IV of Appendix A to verify that 1 L'{arctan(a/s)} =sin at

A:

Q: Find the solutions of the equation that are in the interval [0, 2π).

A: We have the given trigonometric equation as cosπx+sinπx=0

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A: Given: cosu=-23, u terminates in 3rd quadrant We know that if u is in 3rd quadrant then sinu and…

Q: 12. Write an éxpression that gives all sölutions to the equation. COS X - SIn x 3= 2.

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Q: We have - (cos (u) du=

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Q: Find sin 2x, cos 2x, and tan 2x if cos x= and x terminates in quadrant I. 13 sin 2x %3D cos 2x %3D…

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Q: 4 cos* 3xdx

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A: SOLUTION-

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A: the given integral is: ∫cos4x2dx we have to evaluate the given integral.

Q: Evaluate: Je*cos(7e*)cos(4e*)dx.

A: We need to integrate∫excos7excos4exdxSubstitute ex=tDifferentiate x w.r.t texdx=dtThen∫cos7tcos4tdt

Q: Verify.

A:

Q: 2 Arc cos (1- y=

A: Given,   y=2arccos1-x2+4x-x2.   It is differentiated as follows:…

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A:

Q: Differentiate  cos(t^2 - 6)

A: Given: cost2-6

Q: Suppose that π/2≤θ≤π, sin(θ)=2/9, find cos(θ)=______. (round to 3 decimal places)

A: Here, θ is in the second quadrant( π/2≤θ≤π) and cosine is negative in the second quadrant.

Q: Show that the equation has exactly one real root. 2x + cos x = 0

A: