Trig Function Calculator – Calculate Sin Cos Tan Online
Calculate any trigonometric function value including sin, cos, tan, csc, sec, and cot for any angle in degrees or radians with our free online trig calculator.
Trigonometric functions relate angles to ratios of sides in a right triangle. Sine is opposite over hypotenuse. Cosine is adjacent over hypotenuse. Tangent is opposite over adjacent.
The reciprocal functions flip these ratios. Cosecant is 1/sine. Secant is 1/cosine. Cotangent is 1/tangent. They're useful in calculus and physics when the primary functions appear in denominators.
Angles repeat every 360° (or 2π radians). An angle of 390° behaves exactly like 30°. This periodic nature is why trig functions model waves, oscillations, and anything that repeats.
Primary Functions
Reciprocal Functions
Domain and Range
Sign by Quadrant
Mnemonic: "All Students Take Calculus"
| Angle | sin | cos | tan | csc | sec | cot |
|---|---|---|---|---|---|---|
| 0° (0) | 0 | 1 | 0 | — | 1 | — |
| 30° (π/6) | 1/2 | √3/2 | √3/3 | 2 | 2√3/3 | √3 |
| 45° (π/4) | √2/2 | √2/2 | 1 | √2 | √2 | 1 |
| 60° (π/3) | √3/2 | 1/2 | √3 | 2√3/3 | 2 | √3/3 |
| 90° (π/2) | 1 | 0 | — | 1 | — | 0 |
| 180° (π) | 0 | -1 | 0 | — | -1 | — |
| 270° (3π/2) | -1 | 0 | — | -1 | — | 0 |
| 360° (2π) | 0 | 1 | 0 | — | 1 | — |
When is tangent undefined?
Tangent equals sin/cos, so it's undefined whenever cosine equals zero. That happens at 90°, 270°, and every 180° after that. The graph of tangent has vertical asymptotes at these points.
Why are some cosecant and secant values undefined?
Cosecant is 1/sine and secant is 1/cosine. When sine or cosine equals zero, you'd be dividing by zero – which is undefined. Cosecant is undefined at 0°, 180°, 360°. Secant is undefined at 90°, 270°.
How do I convert between degrees and radians?
Multiply degrees by π/180 to get radians. Multiply radians by 180/π to get degrees. A full circle is 360° or 2π radians. So 180° = π rad, 90° = π/2 rad, 60° = π/3 rad.
What does it mean that trig functions are periodic?
Periodic means they repeat their values in regular intervals. Sine and cosine repeat every 360° (2π rad). Tangent and cotangent repeat every 180° (π rad). This is why sin(30°) = sin(390°) = sin(750°).
How do I know which quadrant an angle is in?
First normalize the angle to 0°–360°. Quadrant I is 0°–90°, Quadrant II is 90°–180°, Quadrant III is 180°–270°, Quadrant IV is 270°–360°. The quadrant tells you which functions are positive.
What are exact values vs decimal approximations?
Exact values use fractions and radicals like 1/2 or √3/2. Decimal approximations are rounded numbers like 0.5 or 0.866025. Exact values are precise; decimals are easier to compare but lose precision.
Other Free Tools
Inverse Trig Calculator – Find arcsin arccos arctan Online
Calculate inverse trigonometric functions including arcsin, arccos, and arctan with our free online inverse trig calculator. Get angle results in both degrees and radians.
Degrees to Radians Converter – Convert Angles Online
Convert any angle from degrees to radians or radians to degrees with our free online converter. Instant and accurate angle conversions using π-based formulas.
Trig Identity Verifier – Verify Trigonometric Identities Online
Verify any trigonometric identity online with our free trig identity verifier. Simplifies both sides of an equation to check if the identity holds using fundamental trig rules.
Unit Circle Reference Tool – Interactive Unit Circle Chart
Explore the complete unit circle with our free interactive unit circle reference tool. View all key angles in degrees and radians with their exact trig values and coordinates.
Law of Sines Calculator – Solve Triangles Using Sine Rule
Solve any triangle using the Law of Sines with our free online calculator. Find missing sides and angles for ASA, AAS, and SSA triangle configurations with step-by-step solutions.
Law of Cosines Calculator – Solve Triangles Using Cosine Rule
Solve triangles using the Law of Cosines with our free online calculator. Find missing sides and angles for SSS and SAS configurations with detailed step-by-step solutions.
Right Triangle Calculator – Solve Right Triangles Online
Solve any right triangle by entering two known values with our free online right triangle calculator. Find all sides, angles, area, and perimeter with clear step-by-step solutions.
Triangle Solver – Solve Any Triangle SSS SAS ASA AAS
Solve any triangle completely using SSS, SAS, ASA, or AAS methods with our free online triangle solver. Find all missing sides, angles, and area with step-by-step trigonometric solutions.