What is sin(-240^circ)?

2 Answers
Nghi N
Dec 30, 2016

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

Alan P.
Dec 30, 2016

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:
enter image source here
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

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