Question

How do you evaluate sine, cosine, tangent of `-840^circ` without using a calculator?

Answer 1

`sin = - sqrt3/2`
`cos = - 1/2`
`tan = sqrt3`

Explanation:

Trig unit circle gives:
sin (-840) = sin (-120 - 720) = sin (-120) = - sin (-120 + 180) = - sin (60).
Trig table of special arcs gives:
`sin (-840) = - sin (60) = - sqrt3/2`
`cos (-840) = cos (- 120) = cos (120) = - 1/2`
`tan (-840) = sin/(cos) = (- sqrt3/2)(- 2/1) = sqrt3`