Math III - 7.5 DHQ (3rd) 12/11

Front

What is the equation of the graph for a sine function with an amplitude of 2?

Back

y = 2 sin x

Front

What is the period of the function y = sin(kx)?

Back

The period is given by \( \frac{2\pi}{k} \).

Front

What is the amplitude of the function y = A cos(kx)?

Back

The amplitude is |A|.

Front

Write the equation for a sine function with an amplitude of 6 and a period of \( \frac{\pi}{4} \).

Back

y = 6 sin(8x) (since k = 8 for period \( \frac{2\pi}{k} = \frac{\pi}{4} \)).

Front

What is the amplitude of the function y = -10cos(5x)?

Back

The amplitude is 10.

Front

What is the period of the function y = 2 sin(3x)?

Back

The period is \( \frac{2\pi}{3} \).

Front

What is the equation of the graph for a cosine function with an amplitude of 3?

Back

y = 3 cos x.

Front

How do you determine the period of a trigonometric function?

Back

The period is determined by the coefficient of x in the function, using the formula \( \frac{2\pi}{k} \).

Front

What is the amplitude of the function y = 4 sin(2x)?

Back

The amplitude is 4.

Front

What is the equation of the graph for a cosine function with a period of \( \frac{\pi}{2} \)?

Back

y = cos(4x) (since k = 4 for period \( \frac{2\pi}{k} = \frac{\pi}{2} \)).