Question

15 points

The sign of a 30 degree angle is equal to the cosine of a 60 degree angle.

•True
•False

Answer 1

True

[Assuming you meant sine not sign.]

cosine stands for "complementary sine" meaning the sine of an angle is the cosine of the complementary angle and the cosine of an angle is the sine of the complementary angle. In symbols,

`\sin x = \cos(90^\circ - x)`

`\cos x = \sin(90^\circ - x)`

30 and 60 degrees are of course complementary angles, so this is a true statement.

The question writers in this case availed themselves of one of the two tired triangles of trig, so we know these quantities exactly:

`\sin 30^\circ = \frac 1 2`

`\cos 60^\circ = \frac 1 2`

They're equal.

True.