What is the general value of #theta# satisfying both #sin# #theta# = #-1/2# and #tan# #theta# = #1/(sqrt3)# ?

1 Answer
Nghi N
Apr 27, 2018

#t = +- (5pi)/6 + 2kpi#

Explanation:

#sin t = - 1/2# (1)
#tan t = sin t/(cos t) = 1/sqrt3# (2)
Substitute #sin t = - 1/2# into equation (2).
#- 1/(2cos t) = 1/sqrt3#
Cross multiply:
#2cos t = - sqrt3#
#cos t = - sqrt3/2#
Trig table and unit circle give 2 solutions -->
#t = +- (5pi)/6 + 2kpi#

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