cosh(2æ) – 1 Verify the identity sinh? (x) using the definitions of the hyperbolic functions.

Q: a. Express x = --3-8ż in its trigonometric form r (cos(0) + i sin(0)) with 0 ≤ 0 < 2. Give your…

A: a) x=-3-8ib) 2+5i2+2i

Q: V3 B) If sinh 0 Find cosh 0, tanh 0, coth 0. 2 = %3D

A: Given,  sinhθ = 32  We have to find coshθ, tanhθ  and  cothθ.

Q: ∫cos(7t) dt Evaluate indefinite anti-differentiation

A: LetI=∫cos7tdtPut 7t=uDifferentiate on both side7dt=dudt=du7ThereforeI=∫cosu17duTake the constant…

Q: In( cosh(9x) - sinh(9x) ) - In( cosh(10x) + sinh(10x) ) = Select one:

A: Solution: The objective is to find the value of the given expression

Q: 11. y = sin 12. y = cos*(-) 13. y = arccos(-) %3D 14. y = arcsin (- 5

A:

Q: Sin X-coox +1 senx+l sinx + c00x-1

A: Given data is : To prove the identity, sinx-cosx+1sinx+cosx-1=sinx+1cosx

Q: 2 cos @ dӨ . 1- sin 0

A:

Q: 4. x = 3 + 4 sine, y = 3cos0 - 4

A: Given: x=3+4sinθ, y=3cosθ-4 dxdθ=ddθ3+4sinθ = 4cosθ dydθ=ddθ3cosθ-4 = -3sinθ

Q: 1. Find the first derivative of the given trigonometric function 1 z = 4cos?. 2

A:

Q: Q#2 (a): Find root of the equation 3x + sinx – e* = 0 by secant method correct to six decimal Places…

A: # we are entitled to solve 1 question at a time ,please resubmit the other question if you wish to…

Q: exp in)) (exp(- - ίπ) dxa 0.3679 cos TT - i sin Tt -0.3679 - exp(cos Tt - i sin Tt)

A:

Q: Find the maximum value of sin θ + cos θ.

A: Let  fθ=sin θ+cos θ Differentiate with respect to 'θ', we get f'θ=cos θ-sin θ For maxima or minima,…

Q: Graphs of y = sin 0 and y = cos0 over [0,2π].

A: as we know the value of sin 0 is 0  so the given equation becomes y=0 which forms an x- axis only…

Q: -2n 1 9. Evaluate : de 6+ sine

A: Given, ∫02π16+sinθdθ=2∫0π16+sinθdθ Let us take…

Q: Where does the periodic function f(x) = 2esin (x/2) take on its extreme values and what are these…

A: Consider the function:  fx=2esinx2 The given function will be maximum when sin(x/2) =1 because the…

Q: cos x csc3 x + C sin4 x 1.

A: To evaluate the given integral.

Q: (2) What are the derivatives of the six basic hyperbolic functions? What are the corresponding…

A: Hyperbolic functions are the trigonometric functions defined on parabola instead of taken on the…

Q: Use the graph of y = 2 sin 2x in the figure to obtain the graph of y = 2 csc 2x.

A: The function of the given graph is y=2sin2x. Since, y=sinθ and y=cscθ are reciprocal to each other.…

Q: Evaluate the limit.

A: limt→01-cos2tsin23t

Q: 3 cos° tdt 5. 1+sint

A: Hello! thank you for the question but as per our honor code, we'll able to solve only the first…

Q: - y = sin² (-1) y = cos" - y = arctan 0

A: This question is based on general solution of  Trignometric function.

Q: 1 Proof (I): (sinhx)' = Vx? +1

A: Given: The equation is sinh-1x'=1x2+1. To prove: The main aim is to prove the equation. Concept: The…

Q: cos? (x) 5 x²e* 6 V1 – x³ 4 - ex 7 sinh(x) 8 x² arctan(x) 9 1- X

A:

Q: i. |sin² xcos² xdx

A: We have to find

Q: A cable hangs between two poles of equal height and 24 feet apart. Set up a coordinate system where…

A:

Q: sin(플 + 2x) %3D cos(플 - y) 2- Which of the following is the relationship between x and y according…

A:

Q: what is the period of the function: y=-3 cos (2x-π)? 1. 2 2. 2π 3.π 4. 2π/3

A: Use function of the form y = acos(bx - c) + d

Q: f/² () sin cos (sin (²) dx (Consider initially the first 2 terms)

A: To evaluate: ∫0π2sinx3cos4x3sin2x3dx Let I = ∫0π2sinx3cos4x3sin2x3dx We know that  sinxcosy =…

Q: Y= 5-e- COSX by %3D

A: Given: y=5-e6y=cosx( This question is don't have to specify word  find  and how to find the answer)

Q: sin a COS T Solve by hospital rule lim-

A: after solving we get limit is 1/3

Q: Cos 2x %3D 1-sin 2x

A:

Q: [cos 0 -sin 01, Verify A. AT = I ii. Let A= sin 0

A: We verify that A.A^T = I

Q: ope of the curve 2xy = In(e*) sin(x)

A:

Q: 1. Find the period of the function y = 4 sin () - 3.

A: Concept Used: Consider y=A sin(B(x+C))+D Then Period=2πB radians

Q: Prove the identity. cosh(x) + sinh(x) - e

A: To prove the given identity we uses basic expression for sinh(x) and cosh(x).

Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step:

Q: sin z coS T Q1-Solve by hospital rule lim

A:

Q: ♫♫¹⁄² sin (*) cos (*) sin (²) dx (Consider initially the first 2 terms)

A: Solving the definite integral.

Q: TC In the equation y = sin-1 x, if =;, then y 1 %3D - х,

A: Given: y=sin-1x if x = 12, then  y=sin-112

Q: the slope of the tangent. line to: the graph of y=XT COSXY the point (0,1)? What is of: 4=XT COSメ

A: Given: y=x+cosxy

Q: cos(1339x) cos(1337x)+ sin(1337x) sin(1339x) =?

A:

Q: 3. у %3D tan1(sinh 2x) Зсosh-1 (csc) 4. у %3 CSC

A:

Q: onvert to sine： y=-9.5cos (πx/5)+10.7

A: convert the following into sine

Q: 3. When e is in standard position and its terminal side passes through the point (4, -2) Find the…

A: Given: θ is in standard position and its terminal side passes through point (4,-2)

Q: where does the function 1/sin(x) not exist? what happens if we try to calculate any of these values?

A: We have to find the values where function values doesn't exist.

Q: Cos de 1-Sin e

A: To evaluate: I=∫cos3θ1-sin θdθ=∫cos2θ×cos θ1-sin θdθ=∫(1-sin2θ)cos θ1-sin θdθ=∫(1-sin θ)(1+sin θ)cos…

Q: Solve y' = y3 cos x (Show clear work!)

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: In sine sin -1x os (sin-!x) + C cos V1-x? 1-x² A) True В False

A: To check:  ∫sin(elnsin-1x)dx1-x2=-cos(sin-1x)+C is true or false.