How do you find the general solutions for $csc4x=2$ ?

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Answer 1 · 2015-10-23T03:16:06

Solve $csc (4x) = 2$

Ans: $pi/24$ and $(5pi)/24$

$csc (4x) = 1/(sin 4x) = 2$ --> $sin 4x = 1/2$

Trig Table of Special Arcs gives:
$sin 4x = 1/2$ --> $4x = pi/6$ and $4x = 5pi/6$

a. $4x = pi/6$ --> $x = pi/24$
b. $4x = (5pi)/6$ --> $x = (5pi)/24$

How do you find the general solutions for csc4x=2csc4x=2?