Question #7b11a

1 Answer
Nghi N
Feb 2, 2018

#pi/24; (5pi)/24; (7pi)/24; (11pi)/24#

Explanation:

#4sin^2 (4t) = 1# --> #sin^2 (4t) = 1/4#
#sin (4t) = +- 1/2#
A. #sin 4t = 1/2#
Trig table and unit circle give 2 solutions:
#4t = pi/6#, and #4t = (5pi)/6#
a. #4t = pi/6# --> #t = pi/24#
b. #4t = (5pi)/6# --> #t = (5pi)/24#
B. #sin (4t) = - 1/2#
The unit circle gives 2 solutions:
#4t = (7pi)/6# and #4t = (11pi)/6#
a. #4t = (7pi)/6# --> #t = (7pi)/24#
b. #4t = (11pi)/6# --> #t = (11pi)/24#

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