How do you find the exact value of the sine, cosine, and tangent of the number -10pie/3, without using a calculator?

2 Answers
Nghi N.
Oct 20, 2015

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

Explanation:

The trig unit circle and Trig Table of Special Arcs give -->
#sin ((-10pi)/3) = sin ((-4pi)/3 - 2pi) = sin ((2pi)/3) = sqrt3/2#
#cos ((-10pi)/3) = cos ((2pi)/3) = - 1/2#
#tan ((-10pi)/3) = tan ((2pi)/3) = sin/(cos) = (sqrt3/2)(-2/1) = - sqrt3#

Alan P.
Oct 20, 2015

#sin(-(10pi)/3) =sqrt(3)/2 color(white)("XXXXX")cos(-(10pi)/3)=-1/2color(white)("XXXXX")tan(-(10pi)/3)=-sqrt(3)#

Explanation:

Moving clockwise around the origin we can see that
#-(10pi)/3# is equivalent to a reference angle of #pi/3# in Quadrant II
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The values of #sin(-(10pi)/3)#, #cos(-(10pi)/3)# and #tan(-(10pi)/3)#
follow directly from this diagram and the definitions of these functions

Note: I assumed the "e" in "-10pie/3" was extraneous and not intended to be the natural logarithm base.

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