Question

Find angle theta if the cos is 4/7 and the sin is negative. Please explain in detail if you can!

Answer 1

In which quadrants is sin negative? That's the first thing you need to think about.

Answer 2

Sin is negative in the III and IV quadrants.

Answer 3

So you know it has to be in one of those two quadrants. Out of those 2, which one is cos positive?

Answer 4

Uh, IV

Answer 5

Correct. Now, \[\cos^-1(4/7)=\theta\]

Answer 6

55.15009542

Answer 7

thats cos^-1(4/7)=theta.

Answer 8

That will give you your reference angle. From there, what do you have to do to find what that angle is in the fourth quadrant?

Answer 9

That is where I am lost

Answer 10

Well, the first quadrant is 0-90 degrees. The second 91-180, third 181-270, fourth 271-360.

So if you have an angle of 55, you,re in the first quadrant and you want to go to the fourth. So you want to reflect the angle over the x axis. The x axis can be 0 degrees or 360 degrees. So to move to the fourth, subtract your reference angle from 360.

Answer 11

AH! Thank you! That helps so much.

Answer 12

I remember this now. I forgot I learned it last year

Answer 13

No problem :] Trust me, I know how that feels.

Answer 14

I'm getting all my answers correct on my lesson now! Thank you again :)

Answer 15

You're very welcome. :]