Trigonometric Function Calculator
sin, cos, tan, pi naturally โ use the Visual editor for fractions and roots.
Evaluate: sin(45), cos(pi/3) · Quadrant / Coterminal: just an angle like 210 or 750.
Ready when you are
Type a trig expression above and hit Evaluate.
Calculate to see the unit circle / graph.
Understanding Trigonometric Functions
The six trigonometric functions — sine, cosine, tangent, cosecant, secant, and cotangent — relate angles to ratios of sides in a right triangle. On the unit circle (radius 1, centred at the origin), for any angle θ the coordinates of the terminal point are (cos θ, sin θ). These functions are foundational in physics, engineering, signal processing, and navigation.
Primary Functions
sin θ = opposite / hypotenuse
cos θ = adjacent / hypotenuse
tan θ = opposite / adjacent
Reciprocal Functions
csc θ = 1/sin θ
sec θ = 1/cos θ
cot θ = 1/tan θ
Key Relationships
sin²θ + cos²θ = 1
tan θ = sin θ / cos θ
Period: sin, cos = 2π; tan = π
Special Angle Values
The angles 0°, 30°, 45°, 60°, 90° produce exact trig values using fractions and square roots. Memorising this table is essential for precalculus, calculus, and standardised tests.
| Angle | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 0° | 0 | 1 | 0 | undef | 1 | undef |
| 30° | 1/2 | √3/2 | 1/√3 | 2 | 2/√3 | √3 |
| 45° | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° | √3/2 | 1/2 | √3 | 2/√3 | 2 | 1/√3 |
| 90° | 1 | 0 | undef | 1 | undef | 0 |
Memory trick: sin values for 0°, 30°, 45°, 60°, 90° follow √0/2, √1/2, √2/2, √3/2, √4/2. Cosine is the same sequence reversed.
ASTC Rule — Signs by Quadrant
The mnemonic “All Students Take Calculus” tells which trig functions are positive in each quadrant: Q1 All · Q2 Sine · Q3 Tangent · Q4 Cosine.
1. 150° is in Q2 → reference angle = 180° − 150° = 30°
2. sin(30°) = 1/2
3. In Q2 sine is positive (ASTC: S)
4. sin(150°) = +1/2 ✓