4. Graphing Trigonometric Functions

Determine the value of $y=-2\cdot\sin\left(-\frac{3\pi}{2}\right)+10$ without using a calculator or the unit circle.

Graph the function $y=-3\cdot\cos\left(x\right)$.

Given below is the graph of the function $y=\sin\left(bx\right)$. Determine the correct value for b.

The Period for the function $y=\cos\left(bx\right)$ is $T=20\pi$. Determine the correct value of b.

An object in simple harmonic motion has position function s(t), in inches, from an equilibrium point, as follows, where t is time in seconds.

𝒮(t) = 5 cos 2t

What is the amplitude of this motion?

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 3 - ¼ cos ⅔ x

Match each function with its graph in choices A–I. (One choice will not be used.)

y = cos (x - π/4)

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

G. <IMAGE> H. <IMAGE> I. <IMAGE>

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 3 cos (x + π/2)

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = -sin (x - 3π/4)

Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.

y = 2 cos x

Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.

y = ⅔ sin x

Match each function with its graph in choices A–I. (One choice will not be used.)

y = -1 + cos x

A. <IMAGE> B. <IMAGE> C. <IMAGE>

D. <IMAGE> E. <IMAGE> F. <IMAGE>

G. <IMAGE> H. <IMAGE> I. <IMAGE>

Graph each function over the interval [-2π, 2π]. Give the amplitude. See Example 1.

y = -2 sin x