Question #74a3a

1 Answer
Nghi N
Apr 5, 2017

pi/2; (7pi)/6; (11pi/6)

Explanation:

#2sin t - 1 = 1/(sin t)#
#sin^2 t - sin t - 1 = 0. #
Solve this quadratic equation for sin t.
Because a + b + c = 0, use shortcut. The 2 real roots are:
sin t = 1 and #sin t = c/a = - 1/2#
Use trig table and unit circle:
a. sin t = 1 --> #t = pi/2#
b. #sin t = - 1/2# --> 2 solutions -->
#t = - pi/6#, or #t = (11pi)/6# (co-terminal), and
#t = pi - (-pi/6) = pi + pi/6 = (7pi)/6#
Answers for #(0, 2pi)#:
#pi/2; (7pi)/6; (11pi)/6#

Related questions
See all questions in Solving Trigonometric Equations
Impact of this question
1113 views around the world
You can reuse this answer
Creative Commons License