7.6 Sine and Cosine Curves

Front

What is the period of a sine function with a standard form of y = sin(Bx)?

Back

The period is given by the formula \( \frac{2\pi}{B} \).

Front

What is the amplitude of a sine function?

Back

The amplitude is the maximum distance from the midline of the graph to its peak, represented by the coefficient in front of the sine function.

Front

Write the equation of a sine function with a period of \( \pi \) and amplitude of 7.

Back

The equation is \( y = 7 \sin(2x) \).

Front

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

Back

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

Front

How do you determine the period of a cosine function?

Back

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

Front

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

Back

The amplitude is 5.

Front

If the period of a sine function is \( 4\pi \), what is the value of B in the function \( y = \sin(Bx) \)?

Back

The value of B is \( \frac{1}{2} \).

Front

What is the effect of increasing the amplitude of a sine function?

Back

Increasing the amplitude stretches the graph vertically, making the peaks and troughs higher and lower, respectively.

Front

What is the period of the function \( y = \sin(\frac{1}{2}x) \)?

Back

The period is \( 4\pi \).

Front

What is the relationship between the period and frequency of a sine function?

Back

Frequency is the reciprocal of the period; \( f = \frac{1}{T} \), where T is the period.