How come cosine of 225 degrees is a positive number i thought it was negative because it's reference angle would be 45 degrees below the second quadrant and in a unit circle cosine is just the x value so I thought cosine of something in both the second and third were negative

Question

apparently i'm wrong please explain

Answer 1

225º is in the fourth quadrant, 45º below the first quadrant, so its x value is indeed positive.
Check how angles are measured.

Answer 2

I think i was in radians my bad

um how come tan of 300 is negative root three

tangent in unit circle is y/x I am getting .5/(root three/2)
which is not root three

Answer 3

Forget about my previous post.

Obviously 225º is in the third quadrant, 45º below the second quadrant like you said.
So of course cos 225 is negative.

Answer 4

tan 300º
= -tan 60º by the CAST rule
= -√3/1 from the ratios of the 30-60-90 triangle
= -√3

Answer 5

why wouldn't you use the 30 degree angle?

I did 360 -90 to get 270 degrees and then did 300 - 270 to get 30 degrees and used that angle why would I use the 60 degree angle instead of the thirty

Answer 6

Always ask yourself,
"How far away from the x-axis am I "?
to get the reference angle.

e.g. sin 160
160º is 20º away from the x-axis and according to the CAST rule in quadrant II the sine is positive, so
sin 160º
= sin 20º

e.g. tan 310º
310º is 50º from the x-axis and according to the CAST rule, in quadrant IV the tangent is negative, so
tan 310
= -tan 50

check my examples with your calculator