Question

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

Answer 1

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`