How do you solve $3 csc x = 2 csc x + \sqrt{2}$ $3cscx=2cscx+sqrt2$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

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How do you solve $3 csc x = 2 csc x + \sqrt{2}$ $3cscx=2cscx+sqrt2$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

1 Answer

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Answer 1 · 2016-10-10T18:49:04

$\frac{π}{4}; \frac{3 π}{4}$ $pi/4; (3pi)/4$

Explanation:

Replace in the equation csc x by $\frac{1}{sin x}$ $1/(sin x)$ :
$\frac{3}{sin x} - \frac{2}{sin x} = \sqrt{2}$ $3/(sin x) - 2/(sin x) = sqrt2$
$\frac{1}{sin x} = \sqrt{2}$ $1/(sin x) = sqrt2$ -->
$sin x = \frac{1}{\sqrt{2}} = \frac{\sqrt{2}}{2}$ $sin x = 1/sqrt2 = sqrt2/2$
Trig table and unit circle -->
$x = \frac{π}{4} and x = \frac{3 π}{4}$ $x = pi/4 and x = (3pi)/4$
Answers for $(0, 2 π)$ $(0, 2pi)$
$\frac{π}{4}; \frac{3 π}{4}$ $pi/4; (3pi)/4$

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How do you solve $3 csc x = 2 csc x + \sqrt{2}$ $3cscx=2cscx+sqrt2$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?

1 Answer

Explanation:

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How do you solve 3cscx=2cscx+sqrt23cscx=2cscx+√23cscx=2cscx+sqrt2 for 0<=x<=2pi0≤x≤2π0<=x<=2pi?

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Explanation:

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How do you solve $3 csc x = 2 csc x + \sqrt{2}$ $3cscx=2cscx+sqrt2$ for $0 \leq x \leq 2 π$ $0<=x<=2pi$ ?