Amy's Blog Topic

Reference Angles:
(must be between 0° and 90°)
1)find which quadrant angle is in
2)determine the sign in that quadrant (+ve or -ve)
3)subtract 180° until the angle is between 0° and 90° (0 and π/2)

1)find the reference angle using chart or calculator
2)find what quadrant you need to be in based on the sign of the value
3)use notes to move to that quadrant

**To Move:
I to IV = make negative and add 360°
I to III = add 180°
I to II = make negative and add 180°
II to IV = add 180°

1. The reference angle in the 1st quad is equal to the angle measure.

Example- θ = 60 = 60

2. To find the reference angle in the 2nd quad just subtract the angle from 180°.

Example- θ = 130° = 180° -130°= 50°

3. To find the reference angle in the 3rd quad subtract 180° from the angle given.

Example- θ = 240° = 240° - 180° = 60°

4. To find the reference angle in the 4th quad simply subtracting the angle from 360° will provide the reference angle in the 4th quad.

Example- θ = 315° = 360° -315° = 45°

other examples:

1. sin^-1(-√2/2) = 45°
45 + 180 = 225° = θ
I to IV
-45 + 360 = 315°
θ = 225°, 315°

2. Find the reference angle for sin210°
1. lies in quadrant 3
2. sin is negative in quadrant 3
3. 210-180=30
sin210°= -sin30
you would then look to your trig chart and find a reference to sin 30 (π/6)
sin 210°=1/2