Trig Graphs Review

Front

What is the formula to find the period of a sine graph?

Back

The period of a sine graph can be found using the formula: \( \frac{2\pi}{B} \), where B is the coefficient of x in the function.

Front

What is the equation of a sine graph with an amplitude of 5?

Back

The equation of the graph is: \( y = 5 \sin(x) \) or \( y = 5 \cos(x) \) depending on the phase.

Front

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

Back

The period of the function is \( 2\pi \).

Front

What is the amplitude of the function \( y = 3\sin(7x) - 2 \)?

Back

The amplitude of the function is 3.

Front

Find the period of the function \( y = 2\sin\left(\frac{1}{4}x - \frac{\pi}{2}\right) \).

Back

The period of the function is \( 8\pi \).

Front

What is the amplitude of the function \( y = -5\cos(2x) \)?

Back

The amplitude of the function is 5.

Front

How does the coefficient of x affect the period of a trigonometric function?

Back

The coefficient of x (B) in the function \( y = A\sin(Bx) \) or \( y = A\cos(Bx) \) affects the period, which is calculated as \( \frac{2\pi}{B} \).

Front

What is the effect of a negative sign in front of a sine or cosine function?

Back

A negative sign in front of a sine or cosine function reflects the graph across the x-axis.

Front

What is the phase shift of the function \( y = \sin(x - \frac{\pi}{3}) \)?

Back

The phase shift of the function is \( \frac{\pi}{3} \) to the right.

Front

What is the vertical shift of the function \( y = \sin(x) + 2 \)?

Back

The vertical shift of the function is 2 units upward.