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

1 Answer
KillerBunny
Sep 25, 2015

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.

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