Trig values of any angle

Math

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

  1. Determine which quadrant the angle's terminal side falls in.
  2. Find the reference angle by measuring the acute angle to the x-axis.
  3. Evaluate the trig function using the reference angle.
  4. Apply the correct sign based on the quadrant (All Students Take Calculus).

Examples

  • sin(150°) = sin(30°) = 1/2 because 150° is in Quadrant II where sine is positive
  • cos(240°) = −cos(60°) = −1/2 because 240° is in Quadrant III where cosine is negative
  • 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

Related Terms

Reference angles Unit circle Quadrants Sine cosine tangent

Study This Concept

Practice trig values of any angle with free review games in these units:

Trigonometry Unit 3: Unit Circle