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Chapter 4: Problem 37

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 \(\sin(-t) = -\frac{1}{2}\) and the value of \(\csc(-t) = -2\).

Step by step solution

01

Evaluate \(\sin(-t)\)

Since sine is an odd function, we have \(\sin(-t) = -\sin(t) = -\frac{1}{2}\). So, the value of \(\sin(-t)\) when \(\sin t = \frac{1}{2}\) is \(-\frac{1}{2}\).
02

Evaluate \(\csc(-t)\)

Cosecant is the reciprocal of sine. Therefore, \(\csc(-t) = \frac{1}{\sin(-t)} = \frac{1}{-\frac{1}{2}} = -2\). So, the value of \(\csc(-t)\) when \(\sin t = \frac{1}{2}\) is -2.

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