How do you solve \sin 4\theta = \frac { \sqrt { 3} } { 2}?

2 Answers
Apr 22, 2017

pi/12 + (kpi)/2
pi/6 + (kpi)/2

Explanation:

sin 4t = sqrt3/2
Trig table and unit circle give 2 solutions:

a. 4t = pi/3 + 2kpi
t = pi/12 + (kpi)/2
b. 4t = (2pi)/3 + 2kpi
t = pi/6 + (kpi)/2

sin4theta = sqrt(3)/2

so, 4theta = pi/3 + 2npi or (pi - pi/3) + 2npi for n in ZZ

i.e. 4theta = pi/3 + 2npi or (2pi)/3 + 2npi

=> theta = pi/12 + (npi)/2 or pi/6 + (npi)/2

or, theta = (6n + 1)pi/12 or (1 + 3n)pi/6

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