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Chapter 4: Problem 43

Use the value of the trigonometric function to evaluate the indicated functions. \(\sin t=\frac{1}{2}\) (a) \(\sin (-t)\) (b) \(\csc (-t)\)

Short Answer

Expert verified
The value of \(\sin (-t)\) is \(-\frac{1}{2}\) and the value of \(\csc (-t)\) is \(-2\).

Step by step solution

01

Identifying the given function values

First, get the given value of the sine function, which is \(\sin t = \frac{1}{2}\)
02

Evaluate \(\sin (-t)\)

Next, remember that the sine function is an odd function, meaning that \(\sin(-x) = -\sin(x)\). So, given that \(\sin t = \frac{1}{2}\), it follows that \(\sin (-t) = -\frac{1}{2}\)
03

Evaluate \(\csc (-t)\)

Lastly, remember that the cosecant function is the reciprocal of the sine function, so \( \csc(t) = \frac{1}{\sin(t)} \). Since we've already determined that \(\sin(-t) = -\frac{1}{2}\), it follows that \(\csc(-t) = \frac{1}{\sin(-t)} = -2\)

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