Math / Trigonometry

Question $\sin (\pi / 2)=$ $\square$ and $\sin (3 \pi / 2)=$ $\square$

Studdy Solution

STEP 1

1. The problem involves evaluating the sine function at specific angles.
2. The angles given are in radians.
3. Knowledge of the unit circle and the properties of the sine function is necessary.

STEP 2

1. Evaluate $\sin(\pi/2)$ .
2. Evaluate $\sin(3\pi/2)$ .

STEP 3

To evaluate $\sin(\pi/2)$ , we use the unit circle. The angle $\pi/2$ radians corresponds to 90 degrees, which is located at the top of the unit circle. At this position, the y-coordinate (which represents the sine value) is 1.
$\sin(\pi/2) = 1$

STEP 4

To evaluate $\sin(3\pi/2)$ , we again use the unit circle. The angle $3\pi/2$ radians corresponds to 270 degrees, which is located at the bottom of the unit circle. At this position, the y-coordinate (which represents the sine value) is -1.
$\sin(3\pi/2) = -1$
The values are: $\sin(\pi/2) = \boxed{1}$ $\sin(3\pi/2) = \boxed{-1}$

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