20 POINTS: If tan= 3/4, find the CSC I don't know the relationship between tan and csc, please explain your answer

Step-by-step explanation:

So we know that:

Recall that tangent represents the side opposite over the side adjacent.

This means that the opposite side is 3 while the adjacent side is 4.

Therefore, by using the Pythagorean Theorem, we can solve for the third side, which is the hypotenuse:

Substitute a for 3 and b for 4. Thus:

Square and add:

Square root:

Now, recall that cosecant is the reciprocal of sine. So, find sine first.

Sine is opposite over hypotenuse. From tangent, the opposite is 3 and the hypotenuse as we now know is 5. Thus:

And cosecant is the reciprocal of that. Thus:

And that's our answer :)

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