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

Q: Find the quadrant in which the terminal point detemined by t lies. sin(t)<0 and cos(t)<0…

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Q: Find the solution of the equation cos y ay? which tends to zero as x → 0o and has the value cos y…

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Q: -y = tanh" (cos e* ) ||

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Q: 5. Find the e xact Value. ) sin I Sin( 6. Wtan sint 3.

A: (1) We have to find the exact value of the following -  sin-1sin7π6Since sin-1 and sin together will…

Q: implicitly, if e"(e – 1) + sin(2r + 5y) = In(v7) -- cot(2x) Find

A: Implicit functions are thise functuon in which we can't separate variables. We have to difderentiate…

Q: 1. Find the exact values of sinh (0) and cosh (0) using their definitions.

A: Sinh x=ex-e-x2∴ sinh0=e0-e-02=1-12=0∴sinh0=0      cashx=ex+e-x2∴cash0=e0+e-02=1+12=1⇒cash0=1

Q: 6. Identify the proper trigonometric substitution and then solve the integral 1 dx (x² + 1)²

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Q: 3) If the velocity of a particle moving along a line is given by v(t) = cos = COS 2t), which…

A: We have to find the position expression from the velocity function.         According to our…

Q: 5 sin?(t) cos“(t) dt

A: ∫0π5 sin2t cos4t  dt=5∫0πsin2t. cos2t .cos2t dt=5∫0π sin2t ×1sin2t cos2t dt=5∫0πcos2t…

Q: 口 | 1. What is the frequency of the periodic function 5 sin() f(x) = %3D 3.

A: Given Data: Equation: fx=5sin3θ49 ......1 The general equation of the sinusoidal function.…

Q: 23. Determine the period and amplitude of the function y = 2 sin 5x. 3x D. 2 3x 10 c. 3.2

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Q: Find the amplitude and period for the function y = −2 sin( 12 x).

A: Given:     y=−2sin12x

Q: Find the equation of the tangent line to r = sin3θ  at θ = π/6

A: The equation of the tangent line to a curve y = f(x) is: where m is the slope of the tangent line m…

Q: If cos x is replaced by 1 - (x2/2) and |x |<0.5, what estimate can be made of the error? Does 1 -…

A: We’ll answer the second question first. Notice the question have used first two digits of Maclaurin…

Q: B) Express the given quantity in terms of sin x and cos x sin (플-x)

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Q: (B): Find the tangent equation to the curve y = sin² x at point x = 7. (C): Solve the following…

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Q: 1. S dr 1+sin a+cos a

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

Q: 7. Find the amplitude and period for the function y = -3 sin(4x).

A: Given,           The function is y=-3sin4x .

Q: Which of these will represent u in the function * y= sin -1 Vx2 + 3x + 4? Sin-1 а. du V1-u?

A: Using definition of composite function.

Q: 1. Find of the trigonometric function: dx y=−10x + 3 cosx

A: Derivative of Cosx is -Sinx

Q: d(tan(x)) Using Euler’ formula, show that dx cos x 1.

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Q: find the derivative d/du 1/(1+cos2(u))1/2

A: given:    ddu(11+cos2u)

Q: | 2* (In(4.x))? dr -2х e cos 3x dx

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Q: I co cos (In x) dr

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Q: Eliminate the parameter: x = cos3 t and y = sin3 t.

A: Given: x=cos3t                                               ..1y=sin3t…

Q: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2).

A:

Q: d) Use Newton Raphson method to estimate the root of cos x-xe* = 0, initial guess is

A: To find- Use Newton Raphson method to estimate the root of cosx - xex = 0, initial guess is x0 = 1.

Q: 3. Determine the equation of the sine function shown below: YA y 3 2 30 60 90 120 X IN 11 60 90

A: Given a graph we have to find the equation for sine function. The general function has the equation…

Q: S 1+cos(3x)dx

A: Given : ∫1+cos3xdx

Q: 1. cos x |? ecosx sin xdx

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

Q: .... 2. .... 10 .... 50 Show work: trig ratio (sin, cos, or tan) of L = trig ratio: =7°

A: tan 50∘=pq Here, p represents opposite and q represents adjacent. p=x and q=10 Substitute the value…

Q: Demonstrate and derive the following Bernoulli's Equation. - 2y tan x = y² tan²x dx

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Q: The smallest positive number for which sin(t) - cos(2t) = 0 is t =

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Q: 2/12 6. If sin(t) =- and cos(t) < 0, find the exact value of tan(t). %3D

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Q: Find the derivatives of the functions s = 4/3πsin 3t + 4/5πcos 5t

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Q: B) Express the given quantity in terms of sin x and cos x. Sin (2n – x)

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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: 1- Calculate the value of y if: a- y= sin (0.25) + sinh (2). b- y= sinh (15)+cosh (31)

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

Q: 5. Evaluate 1. , sin(x?) dx

A: #1 intregal

Q: c. Find approximation of the value cos(65") with error less than 5 x 10-5.

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Q: (e) Solve for x 4 + sinh(3x) = 4 cosh(3x). (f) Using Euler's formula, ei = cos 0 +j sin 0, derive…

A: This is a question from hyperbolic functions and complex analysis.

Q: 1. Match th A. Sin В. Cos С. Tan

A: As per the guideline i can answer only first question for you, more than one answer leads me towards…

Q: 4. y = Arc tan² x³ 5. Ø = Are cot 2x

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Q: 4. sin ||

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Q: When a pendulum 0.5 m long swings back and forth, its angular displacement O from rest position, in…

A: Given    Diagram we have a triangle with the vertical angle as Ø, the hypotenuse 50 cm (the…

Q: 17. Determine the equation f(x) = cosx as a sin function.

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Q: Show that y = e²(cos x + sin x) is a solution to the equation

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Q: 12. Find the exact simplified function value of tan (2a). 4 where TTSAL 3T 2. Given sin a= -

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Q: Determine the period as requested. 5) Feriod of y 5 sin 4x A) 4 C)2 -1/2

A: In this question, we want to find the period of the given function.