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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