Question

How do you evaluate the sine, cosine, and tangent of the angle θ = −10π/3 without using a calculator?

Answer 1

Find sin, cos and tan of `((-10pi)/3)`

Explanation:

Trig unit circle -->
`sin ((-10pi)/3) = sin ((-4pi)/3 - 2pi)`=
`= sin ((-4pi)/3) = sin (pi/3) = sqrt3/2`

`cos ((-10pi)/3) = cos ((-4pi)/3 - 2pi) = cos ((-4pi)/3) =`
`= - cos (pi/3) = -1/2`
`tan ((-10pi)/3) = sin/(cos) = (sqrt3/2)(-2/1) = -sqrt3`