MHB Evaluate Trig Expressions....Part 1

[mathdad]

Evaluate the trig expressions using the method shown in the textbook. Steps A through C show the method given in the textbook.

1. sin 210°

A. We are told to graph sin 210°. We are in Quadrant 3.

B. Find the reference angle R.

R = 270° - 210°

R = 60°

C. Evaluate sin R.

sin 60° = -sqrt{3}/2

Book's answer is -1/2.

2. sin (-210°)

A. We are told to graph sin (-210°).
We are in Quadrant 2.

B. Find the reference angle R.

R = -270° - (-210°)

R = -270° + 210°

R = -60

C. Evaluate sin R

sin (-60°) = sqrt{3}/2

Book's answer is 1/2.

 

[skeeter]

1. reference angle for 210 is 30 degrees, not 60. sin(30) = 1/2, but since the reference angle is in quad III where sine is negative, sin(210) = -1/2

2. -210 is coterminal with 150

reference angle is 30 in quad II where sine is positive

sin(30) = 1/2

 

[mathdad]

1. reference angle for 210 is 30 degrees, not 60. sin(30) = 1/2, but since the reference angle is in quad III where sine is negative, sin(210) = -1/2

2. -210 is coterminal with 150

reference angle is 30 in quad II where sine is positive

sin(30) = 1/2

Is there a formula(s) for finding the reference angle and coterminal angle in trigonometry?