How do you solve #sec((3x)/2)+2=0# and find all general solutions?

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How do you solve #sec((3x)/2)+2=0# and find all general solutions?

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Answer 1 · 2016-12-14T14:59:42

#+- (4pi)/3 + (4kpi)/3#

Explanation:

#sec ((3x)/2) = - 2#
#1/cos((3x)/2) = - 2#
#- 2cos ((3x)/2) = 1#
#cos ((3x)/2) = - 1/2#
Trig table and unit circle give as solution arcs:
#(3x)/2 = +- (2pi)/3 + 2kpi#
#3x = +- (4pi)/3 + 4kpi#
#x = +- (4pi)/3 + (4kpi)/3#

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How do you solve #sec((3x)/2)+2=0# and find all general solutions?

1 Answer

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