How do you find the general solutions for $sin 2 θ = cos θ$ $sin 2 theta = cos theta$ ?

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How do you find the general solutions for $sin 2 θ = cos θ$ $sin 2 theta = cos theta$ ?

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Answer 1 · 2018-06-03T23:28:37

$\frac{π}{6}; \frac{π}{2}; \frac{5 π}{6}; \frac{3 π}{2}$ $pi/6; pi/2; (5pi)/6; (3pi)/2$ + $(2 k π)$ $(2kpi)$

Explanation:

sin 2t - cos t = 0
2sint.cos t - cos t = 0
cos t(2sin t - 1) = 0
Either factor should be zero.
a. cos t = 0
Unit circle give 2 solutions
$t = \frac{π}{2}$ $t = pi/2$ , and $t = \frac{3 π}{2}$ $t = (3pi)/2$
b. 2sin t - 1 = 0 --> $sin t = \frac{1}{2}$ $sin t = 1/2$
Trig table and unit circle give:
$t = \frac{π}{6}$ $t = pi/6$ , and $t = \frac{5 π}{6}$ $t = (5pi)/6$
Fro general answer, add $2 k π$ $2kpi$

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How do you find the general solutions for $sin 2 θ = cos θ$ $sin 2 theta = cos theta$ ?

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Explanation:

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Explanation:

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How do you find the general solutions for $sin 2 θ = cos θ$ $sin 2 theta = cos theta$ ?