# Thread: Another Unit circle question

1. ## Another Unit circle question

Can someone explain me these using the unit circle?

cos(180-theta)= -cos theta
cos(-theta)=cos theta
sin(-theta)= -sin theta

Thanks!

2. ## Re: Another Unit circle question

Hello laurettarosa! Are you familiar with the C.A.S.T Rule? Basically, it helps us determine where the trig ratios: sin, cos, and tan are positive or negative.
Let Q = theta.

The C in CAST is located in the 4th quadrant, and only Cosine is positive there.
The A in CAST is located in the 1st quadrant and Sine, Cosine, and Tan are positive there.
The S in CAST is located in the 2nd quadrant and only Sine is positive there
The T is CAST is located in the 3rd quadrant and only Tan is positive there.

Moving on,

cos(180 - Q) : Analysing the angle: 180 - Q, this means that Q is located in the 2nd quadrant and according to CAST, only sine is positive there.
Therefore, cos(180 - Q) = - cos Q

Can you handle the rest? if you have any other questions, please do not hesitate to ask.

3. ## Re: Another Unit circle question

Originally Posted by laurettarosa
Can someone explain me these using the unit circle?

cos(180-theta)= -cos theta
cos(-theta)=cos theta
sin(-theta)= -sin theta

Thanks!
for the first one just look at the picture I made for you. What happens to the x coordinate after you flip it about the y axis.

for the next two it's the same idea but you are flipping it w/respect to the x axis.

Draw a picture like the one I drew for you.