Question #f4496

1 Answer
Nghi N.
Apr 20, 2016

#18^@80; 71^@20; 108^@80; 161^@20#

Explanation:

Replace #cos^2 2x# by #(1 - sin^2 2x)# -->
#4sin^2 2x - 1 + sin^2 2x = sqrt3/2#
#5sin^2 2x = 1 + sqrt3/2 = (2 + sqrt3)/2#
#sin^2 2x = (2 + sqrt3)/10#
#sin 2x = +- sqrt(2 + sqrt3)/sqrt10 = +- 0.61#
a. sin 2x = 0.61 -->calculator and unit circle --> 2 solution arcs -->
#2x = 37^@60 --> x = 18^@80#
#2x = 180 - 37.60 = 142^@40 --> x = 71^@20#
b. sin 2x = -0.61 --> unit circle --> 2 solution arcs -->
2x = - 37.60 (or 322.40, co-terminal arc) --># x = 161^@20#
#2x = 180 + 37.60 = 217^@60 --> x = 108^@80#
Answers for #(0, 2pi)#
#18^@80; 71^@20; 108^@80; 161^@20;#

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