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Chapter 4: Problem 41

Use the value of the trigonometric function to evaluate the indicated functions. \(\sin t=\frac{4}{5}\) (a) \(\sin (\pi-t)\) (b) \(\sin (t+\pi)\)

Short Answer

Expert verified
a) \( \sin (\pi - t) = \frac{4}{5} \), b) \( \sin (t + \pi) = -\frac{4}{5} \).

Step by step solution

01

Identify given value

It is given that \( \sin t = \frac{4}{5} \).
02

Apply trigonometric identity for \( \sin (\pi - t) \)

The trigonometric identity \( \sin (\pi - t) = \sin t \) is used. Substituting the given value \( \sin t = \frac{4}{5} \) into this equation, we find that \( \sin (\pi - t) = \frac{4}{5} \).
03

Apply trigonometric identity for \( \sin (t + \pi) \)

The trigonometric identity \( \sin (t + \pi) = -\sin t \) is used. Substituting the given value \( \sin t = \frac{4}{5} \) into this equation, we find that \( \sin (t + \pi) = -\frac{4}{5} \).

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