Charts & references · 3 min read
Trigonometry Cheat Sheet: SOH CAH TOA, Identities, Values
SOH CAH TOA
- SOH: Sine = Opposite ÷ Hypotenuse
- CAH: Cosine = Adjacent ÷ Hypotenuse
- TOA: Tangent = Opposite ÷ Adjacent
Values for common angles
| Angle | sin (exact) | sin (decimal) | cos (exact) | cos (decimal) | tan (exact) | tan (decimal) |
|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 1 | 0 | 0 |
| 30° | 1/2 | 0.5 | √3/2 | 0.866025403784 | 1/√3 | 0.57735026919 |
| 45° | √2/2 | 0.707106781187 | √2/2 | 0.707106781187 | 1 | 1 |
| 60° | √3/2 | 0.866025403784 | 1/2 | 0.5 | √3 | 1.73205080757 |
| 90° | 1 | 1 | 0 | 0 | undefined | undefined |
Decimals come from the scientific calculator in degree mode.
Key identities
- sin²θ + cos²θ = 1
- tan θ = sin θ / cos θ
- Law of sines: a/sin A = b/sin B = c/sin C
- Law of cosines: c² = a² + b² − 2ab cos C
- radians = degrees × π/180
A worked example
sin 30° + cos 60° = 1
Order-of-operations steps 3 steps
Start: sin(30) + cos(60)
- Function
sin(30) = 0.5 (angle in degrees)→ 0.5 + cos(60) - Function
cos(60) = 0.5 (angle in degrees)→ 0.5 + 0.5 - Add
0.5 + 0.5 = 1→ 1
For the unit-circle picture behind these values read the unit circle and trigonometry basics.
Frequently asked questions
Why is tan 90° undefined?
Because cos 90° = 0 and tan = sin/cos, which would divide by zero.
Degrees or radians?
Use whichever the question uses; the calculator has a DEG/RAD toggle and states the unit in the steps.
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