Trigonometry Calculator
Calculate sin, cos, tan, and other trig functions. Solve right triangles by finding missing sides and angles.
Enter all known variables. The calculator will find the rest if such a triangle is possible.
SOHCAHTOA - Trigonometry Made Easy
Remember the basic trigonometric ratios with the mnemonic SOHCAHTOA:
SOH
sin(θ) = O / H
Sine = Opposite / Hypotenuse
CAH
cos(θ) = A / H
Cosine = Adjacent / Hypotenuse
TOA
tan(θ) = O / A
Tangent = Opposite / Adjacent
Common Trigonometric Values
| Angle | sin | cos | tan |
|---|---|---|---|
| 0° | 0 | 1 | 0 |
| 30° | 1/2 | √3/2 | 1/√3 |
| 45° | √2/2 | √2/2 | 1 |
| 60° | √3/2 | 1/2 | √3 |
| 90° | 1 | 0 | undefined |
Key Trigonometric Formulas
Pythagorean Theorem
a² + b² = c²
For any right triangle
Pythagorean Identity
sin²θ + cos²θ = 1
Always true for any angle
Reciprocal Functions
csc(θ) = 1/sin(θ)
sec(θ) = 1/cos(θ)
cot(θ) = 1/tan(θ)
Angle Sum (Right Triangle)
α + β = 90°
The two acute angles sum to 90°
Frequently Asked Questions
How do I use SOHCAHTOA?
First, identify the sides relative to your angle: the hypotenuse (longest side, opposite the right angle), the opposite side (across from the angle), and the adjacent side (next to the angle, not the hypotenuse). Then choose the ratio that uses your known values to find the unknown.
What's the difference between degrees and radians?
Both are units for measuring angles. Degrees divide a full circle into 360 parts. Radians measure the angle based on the radius of a circle—a full circle is 2π radians. To convert: radians = degrees × (π/180).
Why is tan(90°) undefined?
Tangent equals sin/cos. At 90°, cos(90°) = 0, and division by zero is undefined. Geometrically, this represents a vertical line with infinite slope.
How do I find an angle from a trig value?
Use inverse trigonometric functions (also called arc functions): sin⁻¹, cos⁻¹, or tan⁻¹. For example, if sin(θ) = 0.5, then θ = sin⁻¹(0.5) = 30°.
What information do I need to solve a right triangle?
You need at least two pieces of information (besides the right angle): either two sides, or one side and one acute angle. From these, you can calculate all other sides and angles.
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