How do you solve $csc^2x-cscx-2=0$ between the interval $0<=x<=2pi$ ?

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How do you solve $csc^2x-cscx-2=0$ between the interval $0<=x<=2pi$ ?

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Answer 1 · 2017-02-23T18:57:47

$csc^2 x - 2csc - 2 = 0$
Solve this quadratic equation for csc x.
Since (a - b + c = 0), use shortcut. The 2 real roots are csc x = -1 and $csc x = -c/a = 2$
Convert $csc = 1/(sin)$ to sin x, we get sin x = - 1 and $sin x = 1/2$
a. sin x = - 1 --> x = (3pi)/2
b. $sin x = 1/2$ .
Trig table and unit circle give:
$x = pi/6$ and $x = (5pi)/6$
Answers for $(0, 2pi)$
$pi/6; (3pi)/2, (5pi)/6$

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How do you solve $csc^2x-cscx-2=0$ between the interval $0<=x<=2pi$ ?

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