Posted by **Trig** on Tuesday, November 3, 2009 at 8:27pm.

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

apparently i'm wrong please explain

- Trig -
**Reiny**, Tuesday, November 3, 2009 at 8:33pm
225º is in the fourth quadrant, 45º below the first quadrant, so its x value is indeed positive.

Check how angles are measured.

- Trig -
**Trig**, Tuesday, November 3, 2009 at 8:34pm
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

- OOPS -Trig -
**Reiny**, Tuesday, November 3, 2009 at 8:36pm
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.

- Trig -
**Reiny**, Tuesday, November 3, 2009 at 8:38pm
tan 300º

= -tan 60º by the CAST rule

= -√3/1 from the ratios of the 30-60-90 triangle

= -√3

- Trig -
**Trig**, Tuesday, November 3, 2009 at 8:44pm
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

- Trig -
**Reiny**, Tuesday, November 3, 2009 at 9:03pm
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

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