Precal Unit 7: Writing Sine and Cosine Functions From Graphs

Front

What is the period of a sine or cosine function?

Back

The period is the distance along the x-axis for one complete cycle of the wave. For the function $$y = A \sin(Bx)$$ or $$y = A \cos(Bx)$$, the period is given by $$\frac{2\pi}{|B|}$$.

Front

How do you find the amplitude of a sine or cosine function?

Back

The amplitude is the maximum distance from the midline of the graph to the peak (or trough). For the function $$y = A \sin(Bx)$$ or $$y = A \cos(Bx)$$, the amplitude is given by $$|A|$$.

Front

What is the parent function of the sine function?

Back

The parent function of the sine function is $$y = \sin(x)$$.

Front

What is the parent function of the cosine function?

Back

The parent function of the cosine function is $$y = \cos(x)$$.

Front

If the period of a sine function is 1, what is the value of B?

Back

If the period is 1, then $$B = 2\pi$$ because the period is given by $$\frac{2\pi}{|B|} = 1$$.

Front

If the amplitude of a cosine function is 2, what is the value of A?

Back

If the amplitude is 2, then $$A = 2$$ because the amplitude is given by $$|A|$$.

Front

What is the effect of changing the value of B in the function $$y = A \sin(Bx)$$?

Back

Changing the value of B affects the period of the sine function. The period is given by $$\frac{2\pi}{|B|}$$.

Front

What happens to the graph of a sine function if A is negative?

Back

If A is negative, the graph of the sine function is reflected over the x-axis.

Front

How do you determine the phase shift of a sine function?

Back

The phase shift can be determined from the function $$y = A \sin(B(x - C))$$, where C represents the horizontal shift. The phase shift is $$C$$.

Front

What is the range of the sine function?

Back

The range of the sine function is $$[-1, 1]$$.