Question #9db31

1 Answer
Pablocito
Jul 31, 2017

#theta = pi/2 , 7pi/6 , 11pi/6#

Explanation:

First let x = sin #theta#
#2 x^2 - x - 1 = 0#
Complete the Square after dividing by 2
#x^2 - 1/2 x + 1/16 - 1/16 - 1/2 = 0#
#( x - 1/4 )^2 - 9/16 = 0#
#( x - 1/4 )^2 = 9/16#
#( x - 1/4 ) = +- 3/4#
x = 1 , -1/2
Substituting back
#sin theta = 1 , -1/2#
Taking the inverse sin of both sides
# theta = pi/2 , 7pi/6 , 11pi/6#

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