Precal Unit 4: Trig Graphs and Inverses Review

Front

What is the equation for a cosine function with amplitude 5, period \( \frac{2\pi}{\frac{\pi}{4}} = 8 \), phase shift \( \frac{3\pi}{2} \), and vertical shift 7?

Back

\( y=5\cos\left(\frac{\pi}{4}x-\frac{3\pi}{2}\right)+7 \)

Front

What is the period of the function \( y=5\tan\left(2\theta+\frac{\pi}{4}\right)+1 \)?

Back

\( \frac{\pi}{2} \)

Front

Evaluate the function: \( \arcsin\left(-\frac{1}{2}\right) \).

Back

\( -\frac{\pi}{6} \)

Front

What is the expression for \( \tan\left(\cos^{-1}(4x^2)\right) \)?

Back

\( \frac{\sqrt{1-16x^4}}{4x^2} \)

Front

What is the amplitude of the function \( y=2\cos\left(5\theta+\frac{\pi}{6}\right)-3 \)?

Back

2

Front

Define amplitude in the context of trigonometric functions.

Back

Amplitude is the maximum distance from the midline of the graph to its peak or trough.

Front

What is the formula for the period of a sine or cosine function?

Back

Period = \( \frac{2\pi}{|b|} \) where \( b \) is the coefficient of \( x \) in the function.

Front

What is the range of the function \( y=3\sin(x) \)?

Back

The range is \([-3, 3]\).

Front

What is the vertical shift in the function \( y=5\cos(x)+2 \)?

Back

The vertical shift is 2.

Front

What is the phase shift of the function \( y=4\sin(2x-\pi) \)?

Back

The phase shift is \( \frac{\pi}{2} \) to the right.