In which quadrant does the terminal side of each angle lie?

Question

a. 5pi/4
b. 17pi/8
c. -pi/15
d. 37.3pi

how to figure these out?

Jim Burnell you have been a life saver today!!!!!:) Adv. Algebra Trig. teacher likes to give difficult work without much instruction!!!!!! Thank you, Thank you, Thank you!

Answer 1

The basic quadrants are:

1: 0 to π/2
2: π/2 to π
3: π to 3π/2
4: 3π/2 to 2π

a) 3. 5π/4 is 4π/4 + π/4, or π + π/4, so it's between π and 3π/2. That puts it in the 3rd quadrant.

b) 1. 17π/8 is 16π/8 + π/8, or 2π + π/8. The 2π is a complete rotation (360 degrees), so 17π/8 = π/8, which is between 0 and π/2, so it's in the 1st quadrant.

c) 4. -π/15 rotates BACKWARD into the fourth quadrant. But if you can't see that, you can convert it to a positive angle by adding 2π: 2π - π/15 = 30π/15 - π/15 = 29π/15, which is ALMOST 2π...so it's in the 4th quadrant.

d) 3. When the numbers are big, you just need to find the closest multiple of 2 that is less. In this case, 37.3π = 36π + 1.3π. The 36π is 18 rotations, so it makes no difference. 1.3π is more than π but less than 3π/2 (1.5π), so that puts the angle in the 3rd quadrant.