4. Graphing Trigonometric Functions

Determine the value of $y=\(\sin\[\left\)(-\(\frac{\pi}{2}\]\right\))+50$ without using a calculator or the unit circle.

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.

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 4 sin x

Determine the amplitude of each function. Then graph the function and y = sin x in the same rectangular coordinate system for 0 ≤ x ≤ 2π. y = 1/3 sin x

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)

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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

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