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Chapter 4: Problem 64

Evaluate the sine, cosine, and tangent of the angle without using a calculator. $$-\frac{\pi}{2}$$

Short Answer

Expert verified
The sine of -蟺/2 is -1, the cosine is 0, and the tangent is undefined.

Step by step solution

01

Evaluate the sine function

The sine of angle -蟺/2 is determined by the y-coordinate at that angle on the unit circle, which in this case is -1. Therefore, \( \sin(-\frac{\pi}{2}) = -1 \).
02

Evaluate the cosine function

The cosine of angle -蟺/2 is determined by the x-coordinate at that angle on the unit circle, which in this case is 0. Therefore, \( \cos(-\frac{\pi}{2}) = 0 \).
03

Evaluate the tangent function

The tangent of an angle is the sine of that angle divided by the cosine. In our case, \( \tan(-\frac{\pi}{2}) = \frac{\sin(-\frac{\pi}{2})}{\cos(-\frac{\pi}{2})} = \frac{-1}{0}\). As division by zero is undefined, \( \tan(-\frac{\pi}{2}) \) is undefined.

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