Question #90a30

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2 Answers
JS
Sep 27, 2017

# sqrt(3)/2#

Explanation:

If #sin(theta)=1/2#, we know we have a right triangle with hypotenuse of #2# and an opposite side of #1#. We can use Pythagorean's theorem to find the adjacent side:

#a^2+b^2=c^2#
#1^2+b^2=2^2#
#b^2=3#
#b=sqrt(3)#

Since, #cos(theta)=# adjacent/hypotenuse# =sqrt(3)/2#

Nghi N
Sep 29, 2017

#cos t = +- sqrt3/2#

Explanation:

#sin t = 1/2# . Find cos t
Use trig identity: #sin^2 t + cos^2 t = 1#
#cos^2 t = 1 - sin^2 t = 1 - 1/4 = 3/4#
#cos t = +- sqrt3/2#
On the unit circle, when #sin t = 1/2#, t could be either in Quadrant 1 or in Quadrant 2. Therefor, there are 2 values of cos x
#cos x = +- sqrt3/2#

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