How do you evaluate the sine, cosine, and tangent of the angle θ = − 8π/3 without using a calculator?

1 Answer
Jun 28, 2015

sin(− 8π/3 ) = sqrt3/2
cos(− 8π/3 ) = -1/2
tan(− 8π/3 ) = -sqrt3/3

Explanation:

This is the same as saying:

sine(x) = -480
cosine(x) = -480
tangent(x) = -480

Its a high and non simetric number because it's overlapping. Imagine that the angle completed complete laps over the circle in an interval of 2pi or 360 degrees.

So first, 480/360 so you'll know how many laps occurred. The rest of this division will be the angle we want to discover. The rest is 120. Now, 120 is simetric to 60, so:

sin(120) = sqrt3/2
cos(120) = -1/2
tan(120) = -sqrt3/3