Math
Trig values of any angle.
Definition
Trig values of any angle extend sine, cosine, and tangent beyond acute angles to all angles using the unit circle and reference angles. The sign of each trig function depends on which quadrant the terminal side of the angle lies in.
How it works · 4 phases
Step by step.
- Determine which quadrant the angle's terminal side falls in.
- Find the reference angle by measuring the acute angle to the x-axis.
- Evaluate the trig function using the reference angle.
- Apply the correct sign based on the quadrant (All Students Take Calculus).
Examples
Real-world.
- 1 sin(150°) = sin(30°) = 1/2 because 150° is in Quadrant II where sine is positive
- 2 cos(240°) = −cos(60°) = −1/2 because 240° is in Quadrant III where cosine is negative
- 3 tan(315°) = −tan(45°) = −1 because 315° is in Quadrant IV where tangent is negative
Key Fact
ASTC (All Students Take Calculus): All trig positive in QI, Sine in QII, Tangent in QIII, Cosine in QIV