Let , 4 ,− 7 be a point on the terminal side of θ . find the exact values of cos θ , csc θ , and tan θ .

Ok, you are given a point and you need to find the exact values for

First thing first. We need to see if we are working with a unit circle and find the radius.

How to tell if we are working with a unit circle?
We know is a circle.

We know that to find the radius we can use the following formula:


If we are working with a unit circle.

Lets see if it = 1.




Square both sides now



Since we squared, we have a + and a - but we disregard the - because we do not have - radii 

We can also say


Ok, since r does not equal 1, we are not working with a unit circle but we have found r, which is our radius.

Now that we know the value of r, which is , we need to look at the identities of cos, csc and tan.

The identities:




Now that we know their identities and know the radius of our circle, we can find the exact values of cos, csc and tan.

 



The exact values for cos, csc and tan given the point (4,-7) are:
 

It’s either a or c as the answer.