Thread: how do you find the reference angle of csc, sec, cot

1. how do you find the reference angle of csc, sec, cot

Find two solutions of the equation. Give your answers in degrees and radians.

$\displaystyle csc\ \theta \ \frac{2\sqrt{3}}{3}$

the reference angle is 60 degrees and is located in quadrant 1 or 2.

values in degrees: 60, 120
values in radians: $\displaystyle \frac{\pi}{3}, \frac{2\pi}{3}$

first of all, i don't know how to find the reference angle whenever it is csc, cot, sec. i put sin^-1($\displaystyle \frac{2\sqrt{3}}{3}$); didn't come out right. second i dont understand how they got 60 degrees. i mean once you find the reference angle, which is 60, if it is lower than 180 you subtract it from 180, thus we get 120. but how do we get 60?

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and my second question. another question says $\displaystyle cot\ \theta = -1$

i put in tan^-1(-1) and the reference angle is -45 degrees. the answer is positive 45 degrees. did i do something wrong?

2. well firstly you know that $\displaystyle \csc x = \frac{1}{ \sin x}$

so suppose that $\displaystyle \csc x = A$ where A is just some value
then $\displaystyle \frac{1}{ \sin x} = A$
giving $\displaystyle \sin x = \frac{1}{A}$

does that make sense ?

3. yes, i just plugged in everything and got the reference angle.

but why is 60 degrees listed as an answer?

4. They asked for reference angles in both quadrant 1 and 2.

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cot 45 refer

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