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April 20, 2014

April 20, 2014

Posted by **Dee** on Monday, May 3, 2010 at 7:06pm.

Solve the equation in the interval [0°, 360°).

csc θ = 1 + cot θ

- trig -
**Reiny**, Monday, May 3, 2010 at 10:13pm1/sinθ = 1 + cosθ/sinθ

1 = sinθ + cosθ

1 - sinθ = cosθ

1-2sinθ + sin^2 θ = cos^2 θ

1 - 2sinθ + sin^2 θ = 1 - sin^2 θ

2sin^2 θ - 2sinθ = 0

2sinθ(sinθ - 1) = 0

sinθ = 0, θ = 0,180,360°

or sinθ = 1 , θ = 90°

but,...

since we squared, all our answers must be verified.

since csc x is undefined for x = 0,180, 360 none of those will work

so x = 90°

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