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

225º is in the fourth quadrant, 45º below the first quadrant, so its x value is indeed positive.

Check how angles are measured.

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

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.

tan 300º

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

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

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

To understand why the cosine of 225 degrees is a positive number, let's first clarify a few concepts:

1. Reference angle: The reference angle of an angle in a circle with a range of 0 to 360 degrees is the acute angle formed between the terminal side of the angle and the x-axis.

2. Quadrants: In a standard Cartesian coordinate system, there are four quadrants. Quadrant I is the top right quadrant, Quadrant II is the top left quadrant, Quadrant III is the bottom left quadrant, and Quadrant IV is the bottom right quadrant.

Now, let's analyze the case of 225 degrees:

1. We start by recognizing that 225 degrees lies in the third quadrant, where both the x and y values are negative.

2. The reference angle can be obtained by subtracting the nearest multiple of 180 degrees from the given angle. In this case, the nearest multiple of 180 degrees is 180 degrees itself.

So, the reference angle of 225 degrees is 225 degrees - 180 degrees = 45 degrees.

3. The cosine of an angle in a unit circle is equal to the x-coordinate of the corresponding point on the unit circle.

On the unit circle, the point corresponding to an angle of 45 degrees lies in the first quadrant, where both the x and y values are positive.

Therefore, the cosine of 225 degrees is positive because it shares the same x-coordinate as the angle's reference angle of 45 degrees on the unit circle.