How do you solve $5 cos (2 x) + 1 = 3 cos (2 x)$ $5cos(2x)+1=3cos(2x)$ and find all general solutions?

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How do you solve $5 cos (2 x) + 1 = 3 cos (2 x)$ $5cos(2x)+1=3cos(2x)$ and find all general solutions?

1 Answer

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Answer 1 · 2017-01-23T01:23:38

$\frac{π}{3} = k p$ $pi/3 = kp$
$\frac{5 π}{3} + k π$ $(5pi)/3 + kpi$

Explanation:

5cos 2x + 1 = 3cos 2x
2cos 2x = - 1
cos 2x = - 1/2
Trig table and unit circle give 2 solution arcs:
$2 x = \pm \frac{2 π}{3} + 2 k π$ $2x = +- (2pi)/3 + 2kpi$ --> $x = \pm \frac{2 π}{6} + k π = \pm \frac{π}{3} + k π$ $x = +- (2pi)/6 + kpi = +- pi/3 + kpi$
The arc $\frac{5 π}{3}$ $(5pi)/3$ is co-terminal to the arc $\frac{- π}{3}$ $(- pi)/3$ .
General answers:
$x = \frac{π}{3} + k π$ $x = pi/3 + kpi$
$x = \frac{5 π}{3} + k π$ $x = (5pi)/3 + kpi$

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How do you solve $5 cos (2 x) + 1 = 3 cos (2 x)$ $5cos(2x)+1=3cos(2x)$ and find all general solutions?

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Explanation:

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How do you solve 5cos(2x)+1=3cos(2x)5cos(2x)+1=3cos(2x)5cos(2x)+1=3cos(2x) and find all general solutions?

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Explanation:

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How do you solve $5 cos (2 x) + 1 = 3 cos (2 x)$ $5cos(2x)+1=3cos(2x)$ and find all general solutions?