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

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

Tags

CCSS.HSF-IF.C.7E

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

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

Tags

CCSS.HSF.TF.B.7

Front

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

Back

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

Tags

CCSS.HSF.TF.C.8

Front

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

Back

2

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF.TF.A.4

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.

Tags

CCSS.HSF-IF.C.7E

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.

Tags

CCSS.HSF-IF.C.7E