Over the first two weeks of school we start chapter 7. When Mrs. Robinson first started to show us what to do i knew it was going to be hard. I was right. We began learning the beginning of trig which was converting degrees to radians and vice versa. Then we learned how to find arc lengths, radi, and thetas. The one thing i could really understand had to do with the unit circle and sine and cosine which is called "Reference Angles". Once you learned your unit circle and remembered your quadrants you were set, and not to forget how to find your hypotenuse. Although, there are pathagorean triples to help out with that. The way to do these things are:

Sin- in the coordinate plane as y/r or y/hypotenuse
Cos- in the coordiante plane as x/r or x/hypotenuse

Example - If the terminal ray of an angle from the origin passes through (-4,5) find sin(theta) and cos(theta).

*To find either one you would first find your two points and make the triangle. To find your 3 point (hypotenuse) you use the pathagorean thereom which is a^2 + b^2 = c^2

*For sin find the x, which in this case would be 5. So, 5 would go over the hypotenuse which is Squareroot-41. By the rules you know you can never have a squareroot at the bottom. To get rid of it you multiply both the top and the bottom by the squareroot (41). The ending answer would be:

5Squareroot41/41

*For sin find the y, which would be -4. You would follow the same process. By the end your answer would be:

-4Squareroot41/41

The unit circle has to do with the degrees 90,180,270 and 360. The points for each are:
90degrees - (1,0) Trig Chart: Pi/2 = 90degrees
180degrees - (0,1) Pi = 180degrees
270degrees - (-1,0) 3pi/2 = 270degrees
360degrees - (0,-1) 2pi = 360degrees

--The unit circle has a radius of 1.

Example - sin 270degrees = y/r = 0/1 = 0

Example - cos450degrees ; In order to find the point in the unit circle the degrees must be less than 360. To get lower subtract 360 until number is found.

450-260=90;cos90degrees = x/r = 0/1 = 0

--If your degree is negative, you will go around the circle backwards. For example: cos-95. Instead of being in quadrant two you will be in quadrant three because you go backwards from 360.

Finding reference angle goes off of what we learned before. To do this the rules are:

1. Find the quadrant the angle is in
2. Determine if the trig function is postive or negative.
3. subtract 180degrees from the angle until theta is bewteen 0 and 90 degrees.
4.If it is a trig chart angle plug in

Example - Find the reference angle for sin465.

*Subtract 360 = 105. 105degrees is in quadrant 2. Sin is postive in this quadrant. Subtract 180 from 105

+sin(-75)

*This answer will never be negative because you take the absolute value.

= +sin75degrees

Example - Find the reference angle of sin-45

*Because 45 is already lower than 360 there is no need to subtract. -45 is in quadrant 4 and sin is also negative. Because -45 is also less than 90 there is no need to subtract 180. Take the absolute value which equals

-sin45

*45 is in the trig chart which equals squareroot2/2

This is only a breif explanation of reference angles, but from what we learned there are many other problems and solutions that can be ran across.