Question

What is `sin(-240^circ)`?

Answer 1

`sqrt3/2`

Explanation:

Use the unit circle and trig table -->
The co-terminal angle (reference angle) of `(-240^@)` is `(360^@ - 240^@ = 120^@)`
`sin (-240) = sin 120 = sqrt3/2`

Answer 2

`sin(-240^@)=sqrt(3)/2`
(see below for use of reference angle)

Explanation:

The reference angle is the angle between the angular arm and the X-axis when the angle is drawn in the standard position (i.e. with the base arm along the positive X-axis); as such any reference angle should be in `[0,pi/2]`

Negative angles are measured clockwise from the positive X-axis,
so for the angle `-240^@` we have:

which gives us a reference angle of `60^@` in Quadrant 2 where (according to CAST rules) the `sin` is positive.

`60^@` is one of the standard angles with `sin(60^@)=sqrt(3)/2`

Therefore `sin(-240^@)=+sin(60^@) =sqrt(3)/2`