4. Graphing Trigonometric Functions

Determine the simplest form of an equation for each graph. Choose b > 0, and include no phase shifts. (Midpoints and quarter points are identified by dots.)

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Below is a graph of the function $y=\tan\left(bx\right)$. Determine the value of b.

Below is a graph of the function $y=\cot\left(bx+\frac{\pi}{2}\right)$. Determine the value of b.

Graph each function over a one-period interval.

y = 3 sec [(1/4)x]

Concept Check Match each function with its graph in choices A–F.

7.

8.

9.

10.

11. y = cot (x + π )

4

12.

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Graph each function over a one-period interval.

y = - (1/2) csc (x + π/2)

Graph each function over a one-period interval. See Examples 1–3.

y = tan 4x

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = (1/2)csc (2x - π/4)

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 2 sec(πx - 2π)

Graph each function over a one-period interval.

y = csc (x - π/4)

Graph each function over a one-period interval. See Examples 1–3.

y = 2 tan x

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = 1/3 tan (3x - π/3)

For each function, give the amplitude, period, vertical translation, and phase shift, as applicable.

y = cot (x/2 + 3π/4)

Graph each function over a one-period interval.

y = sec (x + π/4)

Graph each function over a one-period interval.

y = 2 tan (¼ x)