Reference angle — Algebra II, what it means and where it is taught
The acute angle between the terminal side and the x-axis.
Taught in Algebra II.
Where it is taught
Practise this idea
8 questions in the course bank use Reference angle, in Radians & the Unit Circle, Trigonometric Identities & Equations, Inverse Trigonometric Functions.
Problem 1
Find the reference angle for 150°.
Worked answer
30
180-150=30
Problem 2
Find the reference angle for 210°.
Worked answer
30
210-180=30
Problem 3
Find the reference angle for 300°.
Worked answer
60
360-300=60
Problem 4
Solve sinθ=12 for 0° ≤ θ < 360°. Give both answers, smallest first.
Worked answer
30,150
Reference angle 30°
30° and 180-30=150°
Problem 5
Solve cosθ=12 for 0° ≤ θ < 360°. Give both, smallest first.
Worked answer
60,300
Reference angle 60°
60° and 360-60=300°
Problem 6
Find arcsin(-12) in degrees.
Worked answer
-30
Reference angle 30°
Arcsine returns -90° to 90°, so -30°
Problem 7
Find arccos(-12) in degrees.
Worked answer
120
Reference angle 60°
Cosine is negative in quadrant II, so 180-60=120
Problem 8
Find arctan(-1) in degrees.
Worked answer
-45
Reference angle 45°
Negative, so -45°