Question

Use fundamental identities to find the value of the trigonometric function.

Find sin s if cos s = 2/3 and s is in quadrant IV.

Answer 1

Do you know the fundamental ID?

Answer 2

\[\sin ^2x+\cos ^2x=1\]

Answer 3

With that, and the quadrant information, if you know one of the two (sine or cosine) you can solve for the other.

Answer 4

how do you know when to use the identities

Answer 5

when you are told i guess

Answer 6

I meant which identity... sorry

Answer 7

You use them when they let you solve the problem. :) This is a common problem type, so you should recognize it as requiring the Fundamental ID.

Answer 8

Well, you need something that relates sine and cosine. This is the ID that does that.

Answer 9

i wouldn't bother
draw a triangle

Answer 10

triangle drawn

Answer 11

The triangle method will work as well. I think using the ID's is more rigorous, AND you need to be comfortable with them for other topics in trig. Also, if you use the triangle, don't forget what quadrant you are in and make sure the sign of your result is correct.