In Problems 107–116, f(x) = sin x, g(x) = cos x, h(x) = 2x, and p(x) = Find the value of each of the following: 37 109. (f.g) 110. (f-g) 3 107. (f + g)(30°) 108. (f – g)(60°) 111. (foh) 112. (g° p)(60°) 113. (р ° g)(315°) 114. (hof)( 6. 115. (a) Find f 1. What point is on the graph of f? 116. (a) Find g ). What point is on the graph of g? (b) Assuming fis one-to-one*, use the result of part (a) to find a point on the graph of f-!. (b) Assuming g is one-to-one*, use the result of part (a) to find a point on the graph of g¯'. (c) What point is on the graph of y=f(x+ (e) What point is on the graph of y = 2s(x – i f x= "? 6. 3 if x = "? 4

Q: Eliminate n from their equations  X= sin n + tan n and y=sin n - tan n

A: With the help of trigonometric identities we eliminate n from the equations.

Q: Problem E4 Proof that: cos³x+sin³ x cosx+sinx + cos³ x-sin³ x cosx – sinx = 2

A: Given  cos3x+sin3xcosx+sinx+cos3x-sin3xcosx-sinx=2

Q: Problem 10  Evaluate the definite integral:  ∫(2 cos x + 7 sin x) dx=  Upper limit of…

A:

Q: 4. Evaluate sin (x) cos°(x)dx

A: To evaluate the integral

Q: 5. S(sin3x + cos2x)²dx

A: To find : ∫sin3x+cos2x2dx

Q: 6. Solve y sin (x) cos (x) with initial condition y'(7) = 1 and y(7) = 0.

A: y = 1/4 [ x - 1/2 sin2x] +x -π/4

Q: |6. Determine two values of x between 0° and 360° that have sin x 2

A:

Q: 9. Sin 2X dx COS 2X

A:

Q: If y = sin(x + 4) cos(7 – x), then is dx A. sin(2r – 3) B. -sin(7–x) cos(x+4) C. cos(2r – 3) D.…

A: We have to find derivative

Q: In Problems 59-82, solve each equation on the interval 0 s 0 < 2m. 59. 2 cos? 0 + cos 0 = 0 60. sin…

A: We have the given trigonometric function as 2sin2θ-sinθ-1=0 On solving further by calculating…

Q: 9 sin5(x) cos³(x) dx

A:

Q: 15. cos³ 3x 3√√/sin 3x dx

A:

Q: y = sin' x- cos 3 – cos' x cos³

A:

Q: 3. If y = (sin 4x)², find y' %3D a.) 4 sin4x cos 4x b.) -4 sin4x cos 4x c.) -8 sin 4x cos 4x d.) 8…

A: “Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 4. Evaluate 5 cos x dx 3 v2 sin x – 1

A: To evaluate : ∫π6π3 5 cos x32 sin x - 1 dx

Q: If cos x is replaced by 1-²/2 and [x] < 0.5, what estimate can be made of the error? Does 1-²/2 tend…

A: The Maclaurin series of cos x can be defined as: cos x=1-x22+x424-x6720+…. The inequality: y&lt;k is…

Q: Solve sin (x) + sin(x) = 0 on [0, 27]

A:

Q: PROBLEM: Integral of sin²x cos²x dx is equal to A. X+C B. cos2x/16-x/8+C C. x/8-(sin 4x)/32+C D.…

A: We need to find integral.

Q: In Problems 13–20, the displacement d (in meters) of an object at time t (in seconds) is given.(a)…

A: Oscillation, in general, is a periodic fluctuation between two things; in the widest sense,…

Q: 3. Find S sin5 x cos* x dx.

A: Use substitution method

Q: In Problems 35-42, sin 0 and cos 0 are given. Find the exact value of each of the four remaining…

A: Ff

Q: 37. 2(cos x)-/2 sin x dx

A: Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: 1 =dx = V81-(3x+5)? 2 3x+5 -tan- (***) + c 9 o 음sin-1 (3g5) +c 9 o tan-! (**5) +c o sin-l (초5) +c…

A:

Q: Problem 17  Find a particular function which is an antiderivative for:  7x + sec(x)tan(x)

A:

Q: 7. S sin3 4 x cos5 4 xdx

A: To find the integration

Q: Problem 4.13 Find f if f'(0) = 2 sin 0 – sec² 0 -

A:

Q: 5. In problems 1-5, by elimination the constant 'a' and 'b' obtain the DEs for which the following…

A: Given:- y =A sin(A+B)  To find:- Eliminate arbitrary constant A and B obtain Differential equation

Q: In each case find cos(2x) and cos(x/2). Do not use your calculator. 3 and 0 <x < n/2 5' 5 a. cosx =…

A: Given that cos x=3/5 and 0&lt;x&lt;π/2. We need to find cos(2x) and cos(x/2).

Q: In Problems 57–60, write the equation of a sine function that has the given characteristics.57.…

A: We know that the period of sine function is 2π. Also, the amplitude of the function y=sinx is one.…

Q: Find sin 2x, cos 2x, and tan 2x if sin x= sin 2x = cos 2x = = tan 2x 010 X 1 and x terminates in…

A:

Q: Find sin 2x, cos 2x, and tan2.x if sinx= -- 3 and x terminates in quadrant IV. V13 sin 2x cos 2x tan…

A:

Q: Problem 1 Evaluate the indefinite integral.  ∫sin^5(x)cos^4(x)dx= ___________________ +C

A: Given integral can be written as Now, we use following substitution

Q: Problem # 15 7 tan (2x) dx use: tan²x = sec² x - 1

A:

Q: IFS(x) = - sin(x), then S ® (1) is equal to - sin(x) B) - cos(x) sin(x) O cos(x)

A: We have to solve

Q: 7 sin(x) -dx 2 cos x+5cos(x)– 3 4.

A:

Q: 2. Find a reduction formula for sin" x dx. By using this formula evaluate sin® x dx.

A: The objective of the question is determine the integral.

Q: 1. Solve the DE: (cos y- cos x)y' +cos y sin 2x = 0

A:

Q: In problems 1-5, by elimination the constant 'a' and 'b' obtain the DEs for which the following…

A:

Q: Question 8 Integrate the function. dx V9 - x2 COs:1 X+C 2 cos x+ sin x+C D sin *-C Question 9 413

A:

Q: 4,5in3x =sinx S Sinx(sin?x-\= sin?x. Sinx(sinx-1). COS X tank (sin zx - COS tan-o TT

A:

Q: 6. S cos32x sin*2xdx

A:

Q: Problem 5 Evaluate the definite integral.  ∫sin^2(6x)cos^2(6x)dx=__________________  (upper limit=7,…

A: Evaluate the integral

Q: Suppose y=sin x, what is x-value between 2pi and 4 pi corresponding to y-value of -1

A:

Q: (9) ſ cos(x²) 2xdx sin x? + c cos x2 + c Option 1 Option 2 sin 2x + c

A: We will substitute  x2 = t

Q: Problem # 2 3 sin x If f(x) = 3 + cos x Find f'(x) =

A: We will find f'(x) as following.

Q: 22) In Problems 22 through 24, given an Implicit Equation 2x3+3y2= 6 sin y + 16 , find y'=, A)…

A: "Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: What’s different between the solutions to the problems cos(x)=1/2 and =cos^-1(1/2)?

A:

Q: Where does the periodic function ƒ(x) = 2e^(sin (x/2)) take on its extreme values and what are these…

A: Given,

Q: Problem 1. (a) Show that that 1 – tanh² x = sech² x and use it to prove that sech(tanh x) = v1 – x².

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: 9. (2 sin x – 3 cos x) dx • T/2 - T/2 -

A: We use Trigonometry table for final answer  and cos(-x) = cos(x)  sin(-x) = -sin(x)