Trigonometry Calculator (Sin, Cos, Tan & Radians)
Calculate sine (sin), cosine (cos), and tangent (tan) of any angle in degrees, and convert degrees to exact π radians.
About the Trigonometry Calculator (Sin, Cos, Tan & Radians)
Trigonometry studies the relationships between the angles and side lengths of triangles and periodic waves on the unit circle. The three primary trigonometric functions are Sine (sin), Cosine (cos), and Tangent (tan).
Our Trigonometry Calculator evaluates sin, cos, and tan for any angle in degrees and converts angles between degrees and exact π radians.
SOHCAHTOA & Degree-to-Radian Formulas
In a right triangle and on the unit circle:
sin(θ) = Opp/Hyp | cos(θ) = Adj/Hyp | tan(θ) = Opp/AdjRadians = Degrees × (π / 180°)sin²(θ) + cos²(θ) = 1How to Evaluate Trigonometric Functions & Convert to Radians
- Convert Degrees to Radians: Multiply the angle in degrees by
π / 180and reduce the fraction using the GCD. - Use Special Unit Circle Angles: Recall exact values for 0°, 30° (π/6), 45° (π/4), 60° (π/3), and 90° (π/2).
Worked Example: For 30°, converting to radians gives 30 × π/180 = π/6 ≈ 0.5236 rad, and sin(30°) = 1/2 = 0.5.
Frequently Asked Questions (FAQ)
Why is tan(90°) undefined?
Because tan(θ) = sin(θ) / cos(θ). At 90°, sin(90°) = 1 and cos(90°) = 0, and division by zero is undefined.
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