Question

How do you tell whether the value of sin (-45 degrees) is positive, negative, zero or undefined?

Answer 1

It's negative.

Explanation:

First of all, the sine function is defined all over the real set, so there's no chanche that `\sin(-45°)` is undefined.

Now, you can solve the problem in a geometrical way: since the sine of an angle is the `y`-coordinate of the point of the unit circle related to that angle, you can clearly see that angles from `0°` to `180°` have a non-negative sine value, while angles from `180°` to `360°` have a non-positive value. Since an angle of `-45°` describes the same point as an angle of `360-45=315°`, we are in the second case, and the sine is positive.

If you want to see it using the definition, the point in the unit circle identified by a `-45°` angle is `(sqrt(2)/2, -sqrt(2)/2)`, so its `y`-coordinate is negative.