SOH CAH TOA
sin θ = opposite ÷ hypotenuse
cos θ = adjacent ÷ hypotenuse
tan θ = opposite ÷ adjacent
Common angles to remember
| Angle | sin | cos | tan |
|---|
| 0° | 0 | 1 | 0 |
| 30° (π/6) | 1/2 | √3/2 | √3/3 |
| 45° (π/4) | √2/2 | √2/2 | 1 |
| 60° (π/3) | √3/2 | 1/2 | √3 |
| 90° (π/2) | 1 | 0 | undefined |
Signs in each quadrant
On the unit circle, cosine is the x-coordinate and sine is the y-coordinate. In quadrant I (0°–90°) all values are positive. In II only sine is positive, in III only tangent, and in IV only cosine. The phrase "All Students Take Calculus" helps you remember the order.
Inverse functions return one angle
arcsin gives an angle between −90° and 90°, arccos between 0° and 180°, and arctan between −90° and 90°. Other angles can share the same ratio (sin 30° = sin 150°), so check which one fits your problem.
Solving a whole triangle? Use the triangle calculator. For longer expressions, the scientific calculator has every trig key.
Last reviewed October 2026.
Frequently asked questions
What are sine, cosine and tangent?
In a right triangle, sine is the opposite side divided by the hypotenuse, cosine is the adjacent side divided by the hypotenuse, and tangent is the opposite side divided by the adjacent side. The memory aid SOH CAH TOA helps you remember them.
What are cosecant, secant and cotangent?
They are the reciprocals: csc = 1 ÷ sin, sec = 1 ÷ cos and cot = 1 ÷ tan. They are undefined where the function they flip is zero, for example csc(0°) and sec(90°).
How do I find an angle from a ratio?
Use the inverse functions: sin⁻¹ (arcsin), cos⁻¹ (arccos) and tan⁻¹ (arctan). Choose "Find the angle", pick the function and enter the ratio. arcsin and arccos only accept values from −1 to 1.
How do I convert between degrees and radians?
Multiply degrees by π/180 to get radians, or multiply radians by 180/π to get degrees. 180° equals π radians, about 3.1416. The calculator shows the angle in both units.
Why is tan(90°) undefined?
tan = sin ÷ cos, and cos(90°) = 0. Dividing by zero is undefined, so tan(90°), tan(270°) and so on have no value.