Find csc 0, sin 0, and cot 0, where is the angle shown in the figure. Give exact values, not decimal approximations.
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Answers:

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Explanation:

Before we can find the trig ratios, we need to determine the length of the missing side. Apply the pythagorean theorem

The vertical side is units long.

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The side we just found is the opposite side to angle (greek letter theta)

The hypotenuse is 7 units long. The hypotenuse is always opposite the right angle.

Divide the hypotenuse over opposite to get the cosecant.

Note: In the third step, I multiplied top and bottom by sqrt(33) to rationalize the denominator.

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Recall that sine is the reciprocal of cosecant, and vice versa.

So we'll use the same idea as before, but flip the original fraction.

The denominator is already a rational number, so there's not much else to do here.

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Cotangent is the ratio of adjacent over opposite

The steps are pretty much nearly identical as the section involving csc, except we're using the adjacent in place of the hypotenuse (so that means we use 4 in place of 7).

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