Trigonometric Functions Math Example 1

Follow the full solution, then compare it with the other examples linked below.

Example 1

easy
Evaluate sinโก(ฯ€6)\sin\left(\frac{\pi}{6}\right) and cosโก(ฯ€6)\cos\left(\frac{\pi}{6}\right).

Solution

  1. 1
    Convert the angle mentally: ฯ€6\frac{\pi}{6} radians equals 30โˆ˜30^\circ.
  2. 2
    Recall the special-angle values from the unit circle or a 3030-6060-9090 triangle: sinโก(30โˆ˜)=12\sin(30^\circ) = \frac{1}{2}.
  3. 3
    Using the same reference triangle, cosโก(30โˆ˜)=32\cos(30^\circ) = \frac{\sqrt{3}}{2}.

Answer

sinโก(ฯ€6)=12,cosโก(ฯ€6)=32\sin\left(\frac{\pi}{6}\right) = \frac{1}{2}, \quad \cos\left(\frac{\pi}{6}\right) = \frac{\sqrt{3}}{2}
The special angles (30ยฐ,45ยฐ,60ยฐ30ยฐ, 45ยฐ, 60ยฐ) and their radian equivalents appear frequently. Memorizing the unit circle values or using the 30-60-90 and 45-45-90 triangle ratios is essential.

About Trigonometric Functions

Trigonometric functions (sin, cos, tan, etc.) relate angles in right triangles to side ratios and extend to periodic functions of real numbers via the unit circle.

Learn more about Trigonometric Functions โ†’

More Trigonometric Functions Examples

Example 2 medium

Find the exact value of [formula].

Example 3 easy

Evaluate [formula].

Example 4 hard

If [formula] and [formula] is in Quadrant II, find [formula] and [formula].

โ† All Trigonometric Functions Examples Trigonometric Functions Concept