Question #47674

1 Answer
Nghi N
Feb 27, 2018

#pi/2; (3pi)/4 (3pi)/2; (7pi)/4#

Explanation:

#sin 2t + cos^2 t = 0#
Replace sin 2t by 2sint.cos t (identity)
#2sin t.cos t + cos^2 t = 0#
#cos t(2sin t + cos t) = 0#
Either factor should be zero.
a. cos t = 0 --> Unit circle gives 2 solutions -->
#t = pi/2#, and #t = (3pi)/2#
b. 2sin t + cos t = 0
Divide both sides by cos t
2tan t + 1 = 0
tan t = - 1
Unit circle gives 2 solutions -->
#t = (3pi)/4# and #t = (3pi)/4 + pi = (7pi)/4#

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