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madreJ [45]
3 years ago
8

Identify the beginning of a sample period for the function: : f(t)=2csc(t+pi/4)-1

Mathematics
1 answer:
tamaranim1 [39]3 years ago
5 0
ANSWER

- \frac{\pi}{4}

EXPLANATION

The given function is,

f(t) = 2 \csc(t + \frac{\pi}{4} ) - 1

This function has a period of
2\pi
just as the parent function

f(t) = \csc(t )

A sample period of this parent function is

[ 0 , 2\pi]

Which begins at zero.

For the transformed function,

f(t) = 2 \csc(t + \frac{\pi}{4} ) - 1
There has been a horizontal shift of
\frac{\pi}{4}
to the left.

The transformed function will have a sample period,

[ - \frac{\pi}{4} , \frac{7\pi}{4} ]

Therefore a sample period begins at

- \frac{\pi}{4}
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