By applying the first shift theorem, calculate the following functions; (i) L = {e=2{cos 6t} (ii) Based on your understanding, explain why the first shift theorem needs to be applied to solve the function.

Q: Use a graphing utility to approximate (to three decimal places) the solutions of the equation cos2 x…

A:

Q: Find the range, periodicity and phase shift of y = 2 sin (x + 3)

A:

Q: Give an equation of the resulting function when y=cosθ is horizontally compressed by a factor of 1/4

A: Step:I:          Given an equation of the resultin functions      When y=cosθ is horizontally…

Q: Find the period, amplitude, and phase shift of the function.   y= -3 - 4 sin( 3x - (π/4) ) Give the…

A:

Q: Give an equation for a transformed sine function with an amplitude of 3, a period of , and a phase…

A:

Q: Determine the phase shift and vertical shift of the following function. "(9) 3D -좋 cos(10 + 20")-홀

A: fθ=-23cos12θ+20-32 fθ=-23cos12θ+40-32 fθ=-23cos12θ--40-32

Q: > Question 1 of 16 27T Find an equation of the tangent line to f(x) = 7 cos(x) at x = 3 (Let y f(x)…

A: To determine the equation of the tangent line.

Q: Give an equation for a transformed sine function with an amplitude of a period of, and a vertical…

A: In the given problem we have to find an equation for a transformed sine function with an amplitude…

Q: Find the exact simplified Function value COs cos/

A: To find

Q: Find the exact circular function value of cos (-2π/3)

A: Given,

Q: Find the amplitude, period, or phase shift as specified. Find the period of y = -4 sin 6x-

A:

Q: Determine the amplitude, period, and phase shift of y = 4 sin(2πx + 2). Then graph one period of the…

A: Consider the function: y=4sin2πx+2…

Q: 14. у %3D Sin-1 (Зх - 1) -3 3 Od. T-9x +6x Зх-1 O0. -9x+6x OCT-9x+6x Oa. V1-(3x-1)

A: Let's find.

Q: Find the amplitude, period, and phase shift of y = 3 / 2 cos (6x + 3π). Graph the function, showing…

A: Given the cosine function y=32cos(6x+3π)

Q: Find all solutions of the equation. COS X=

A: The given equation is cos x=-12

Q: Solve for θ.  sinθ=cos(2θ−30°)

A: We use the following formula

Q: Suppose y = -6 cos (5t + 10) – 5. In your answers, enter pi for T. What is the horizontal shift?

A: Horizontal shift

Q: Suppose the function cos(t) is shifted 5 units upward. What is the equation of the new function?

A: To determine The equation of the new function if the function cos(t) is shifted 5 units upward.…

Q: Find the amplitude, period, and phase shift of the function. y = -4 sin(x -) amplitude period 2n…

A:

Q: 13. Write a sine function with a horizontal shift of h=1.

A:

Q: Write an equation for a function with the given characteristics. A sine curve with a period of 4, an…

A: Given that the amplitude= 2. So, A=2 Period = 4π, so, B=2π/ period= 2π/4π = 1/2  Left phase shift=…

Q: Find the amplitude, period, and phase shift of the function. =I 1 sin (3x-x)+3 Give the exact…

A:

Q: Find the amplitude and period of the function. (=cos(6x) - cos(6x) amplitude period Sketch the graph…

A:

Q: Determine the amplitude, period, and phase shift of the function y= (5/2) sin (2x + π/2). Then graph…

A: Given function, y=52sin2x+π2 The general form of sine function is given by, y=asinbx+c+da=…

Q: Write an equation in terms of x and y for the function that is described by the given…

A:

Q: The phase shift of the graph of f(t) = sin (4t - TT) is? %3D

A: We have to find phase shift of the graph of function: ft=sin 4t-π Drawing the graph of given…

Q: Determine the amplitude, period, and phase shift of y = 4 sin(2mx + 2). Then graph one period of the…

A: we have general equation of Sine as y=asin(bx-c)+d comparing with y=4sin(2πx+2) Here, a=4 b=2π c=-2…

Q: Use the graph of the sine to sketch one period of the graph of the function. y = −1 + 2 sin(2x…

A: It is given that, y=-1+2sin2x-π2 It is known that, if f(x) has period P, then function f(ax+b) has…

Q: Find the general solution of the equation: cos.xr-sin 2x = 0

A: NOTE: Refresh your page if you can't see any equations. . use the formula  factor out

Q: Determine an equation, in simplified form, for the family of quartic function with COS 3 and 2 + √5

A: In this question, the concept of the polynomial is applied. Polynomial The term "polynomial" refers…

Q: Write an equation for a function with the given characteristics. A sine curve with a period of 81,…

A:

Q: Find the amplitude, period, or phase shift as specified. Find the period of y = -4 sin 6x •.

A: y=-4sin6x+π2---------------------1standard equation of sinosidal function…

Q: Determine the amplitude, period, and phase shift of y = -2 cos(2x - π/2). Then graph one period of…

A: We have to find amplitude, period and phase shift of the function: y=-2 cos2x-π2 also have to draw…

Q: Determine the amplitude, period, any vertical translation, and any phase shift of the given graph. y…

A:

Q: Determine the amplitude, period, and phase shift of the function y = -3 sin(2πx + 4π). Then graph…

A:

Q: Find the equation of the cos function whose graph is the graph of y = - 2 cos 2(x-pi/4)+1 shifted…

A: We have to find the equation of the cos function whose graph is the graph of y=-2cos2x-π4+1 shifted…

Q: Use a calculator to solve the equation cos x = -2/5 correct to four decimal places, on the interval…

A: Given equation is cosx=-25. Solving the given equation. cosx=-25x=cos-1-25x=113.5781°

Q: Write the function of the form y = sin bx corresponding to the given period. Period: 4

A: Periodicity

Q: Find the equation of the following sine wave in its final position. The graph of y= cos (x) is…

A: Given :   Shifted pi/5 units to the left

Q: Find the range, periodicity and phase shift of y = 2 sin (;x + 3)

A: We need to find the range, periodicity, phase shift of y=2sin((1/2)x+3).

Q: 1. 3 cos x = x +1

A:

Q: Using Newton Raphson method, find a root correct to 3 decimal places of the following. xe* – cos x =…

A:

Q: Determine the amplitude, period, and phase shift of the function y = -2 sin(2x + π/2). Then graph…

A: We know that, For a function y = m sin [n(x + r)] +s Amplitude is m Period is 2π/n Phase shift is r

Q: Use an identity to solve the equation 2 cos2 x - sin x - 1 = 0 on the interval [0, 2π).

A:

Q: Determine the amplitude and period of the function y = -2 cos 2x. Then graph one period of the…

A: The amplitude (A) of a function y = a cos(bx) is given by: A = mod a The period (p) of a function y…

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

A: