reference angles?

Simona Bulwinkle: Basically, if you can visualize which quadrant the angle (let's call it "θ") would be in, then you're all set. Remember, the first quadrant is from 0 to 90 degrees (0 to pi/2); the second quadrant is from 90 deg to 180 deg (pi/2 to pi); the third quadrant is from 180 deg to 270 deg (pi to 3pi/2); and the fourth quadrant is from 270 deg to 360 deg (3pi/2 to 2pi)(BTW, It's easier to see why the following equations work, if you draw a picture. Just draw a cross on your paper, and you've got the 4 quadrants!)If θ is in the 1st quadrant, then you've already got the reference angle. If θ is in the 2nd quadrant, then calculate 180 deg - θ (or pi - θ)If θ is in the 3rd quadrant, then it's θ - 180 deg (or θ - pi)If θ is in the 4th quadrant, then it's 360deg - θ (or 2pi - θ)IF the given angle is bigger than 360 deg (or 2 pi), then keep on subtracting 360 deg (2 pi) until you get the smallest positive angle. Then follow the steps above.IF the given a! ngle is a negative angle, then keep on adding 360 deg (or 2 pi) until you get the smallest positive angle, then follow the steps above.So....1) 185 degrees is in the 3rd quadrant. 185 deg - 180 deg = 5 deg. 5 deg is the reference angle.2) 320 deg is in the 4th quadrant. 360 deg - 320 deg = 40 deg. 3) -145 deg is negative, so let's add 360 degrees...-145 + 360 = 215 deg. 215 deg is in the 3rd quadrant. 215 - 180 = 35 deg4) -290 deg is negative, so let's add 360 degrees.-290 + 360 = 70 deg. 70 degrees is in the 1st quadrant... so that's your reference angle.5) 3pi/4 is in the 2nd quadrant. So: pi - 3pi/4 = pi/46) -pi is negative, so let's add 2pi.-pi + 2pi = pi. That's right on the negative x-axis... the reference angle is 0.-------------------------------BTW, just some things to remember...1) If you do draw a picture, make sure that you ARE NOT calculating the angle in reference to the y-axis... (a very common mistake)2) Just remember that your reference angle has t! o be less than 90 deg (or pi/2). If it's bigger, then you've ! miscalculated......Show more