Unit 4 test: Graphs of Trigonometric Functions

Find $\cos(5\pi)$ using the periodicity of cosine.

How many zeros does $y = \sin x$ have on the closed interval $[0, 2\pi]$?

What is the amplitude of $y = -5\cos\left(\dfrac{x}{2}\right) + 1$?

What is the period of $y = 3\sin(4x)$? (You can type pi.)

What is the phase shift of $y = \cos(3x - \pi)$? Give a positive number for a shift to the right and a negative number for a shift to the left.

What is the range of $y = 2\sin x + 3$?

Which equation matches the graph?

What is the period of $y = \tan\left(\dfrac{x}{3}\right)$?

What is the smallest positive $x$-value of a vertical asymptote of $y = \tan\left(x + \dfrac{\pi}{6}\right)$?

Which function has vertical asymptotes at $x = k\pi$ and branches that decrease from left to right?

Evaluate $y = 4\sec x$ at $x = \dfrac{\pi}{3}$.

What is the range of $y = \sec x + 1$?

At a harbor, high tide occurs at 1:00 p.m. and the next low tide occurs at 7:15 p.m. Assuming the tide is sinusoidal, what is the period of the tide in hours?

The depth of water at a dock, in feet, is modeled by $d(t) = 3\cos\left(\dfrac{\pi}{6}(t - 1)\right) + 7$, where $t$ is hours after midnight. What is the depth at $t = 5$?