How do you solve sec((3x)/2)+2=0sec(3x2)+2=0 and find all general solutions?

1 Answer
Nghi N
Dec 14, 2016

+- (4pi)/3 + (4kpi)/3±4π3+4kπ3

Explanation:

sec ((3x)/2) = - 2sec(3x2)=−2
1/cos((3x)/2) = - 21cos(3x2)=−2
- 2cos ((3x)/2) = 1−2cos(3x2)=1
cos ((3x)/2) = - 1/2cos(3x2)=−12
Trig table and unit circle give as solution arcs:
(3x)/2 = +- (2pi)/3 + 2kpi3x2=±2π3+2kπ
3x = +- (4pi)/3 + 4kpi3x=±4π3+4kπ
x = +- (4pi)/3 + (4kpi)/3x=±4π3+4kπ3

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