Steps:
- Find the quadrant then sketch.
- Find out if the angle is + or -.
- Subtract either 360 degrees or 180 degrees until the absolute value of theta is between 0 and 90 degrees.
1. First, you have to subtract 180 from 400 to find out what quadrant it is in. When you subtract you get 220. That is in the third quadrant.
2. To find out if is it + or -, you do y/r. The radius is always one. So you end up with -/1 which is -. The reason the top number is - is because the y coordinate in the third quadrant is -. So it is going to be -.
3. Now to find the reference angle of this problem, you have to subtract 220 from 180. When you subtract you get 40.
Your final answer is sin400 degrees = -sin40 degrees.
Ex. 2 Explain cos7pi/4 as a reference angle.
1. First of all you need to put the problem in degrees. To do that you take 7pi/4 and multiply it by 180/pi. When you do this pi will cancel and leave you with 315 degrees. So now your problem is cos315 degrees. Now we can find what quadrant it is in. It is in quadrant four.
2. Now you need to find out if it is + or -. Cos is x/r. So x/r = +/1 = +.
3. Now you have to subtract 315 from 360 which gives you -45. You then take the absolute value of that which is 45.
Your final answer is cos315 degrees = +cos45 or cos7pi/4 = +cospi/4.
Ex. 4 Evaluate sin60 degrees.
The only thing you have to do for this problem is go to your trig chart and find sin60 degrees. According to the trig chart, sin60 degrees is the square root of 3/2. So sin60 degrees = square root of 3/2.
-Amber :)
Amber,
ReplyDeleteI like that you included a radian problem in your blog. Great work!