Trig Values Table
A complete interactive reference table and custom solver for trigonometric values. View exact fractional and radical values for sin, cos, tan, csc, sec, and cot for all standard unit circle angles from 0° to 360° (and their radian equivalents). Calculate values for any custom angle and visualize vectors on our dynamic unit circle diagram.
Interactive trigonometric reference chart. Input any angle in degrees or radians to calculate standard and exact fractional values for all 6 trig functions, and visualize the corresponding vector and projections on the interactive Unit Circle.
Standard Angles Trigonometry Table (0° - 360°)
Click row to solve angle| Degrees | Radians | sin θ | cos θ | tan θ | csc θ | sec θ | cot θ |
|---|---|---|---|---|---|---|---|
| 0° | 0 | 0 | 1 | 0 | Undefined | 1 | Undefined |
| 30° | π/6 | 12 | √32 | √33 | 2 | 2√33 | √3 |
| 45° | π/4 | √22 | √22 | 1 | √2 | √2 | 1 |
| 60° | π/3 | √32 | 12 | √3 | 2√33 | 2 | √33 |
| 90° | π/2 | 1 | 0 | Undefined | 1 | Undefined | 0 |
| 120° | 2π/3 | √32 | -12 | -√3 | 2√33 | -2 | -√33 |
| 135° | 3π/4 | √22 | -√22 | -1 | √2 | -√2 | -1 |
| 150° | 5π/6 | 12 | -√32 | -√33 | 2 | -2√33 | -√3 |
| 180° | π | 0 | -1 | 0 | Undefined | -1 | Undefined |
| 210° | 7π/6 | -12 | -√32 | √33 | -2 | -2√33 | √3 |
| 225° | 5π/4 | -√22 | -√22 | 1 | -√2 | -√2 | 1 |
| 240° | 4π/3 | -√32 | -12 | √3 | -2√33 | -2 | √33 |
| 270° | 3π/2 | -1 | 0 | Undefined | -1 | Undefined | 0 |
| 300° | 5π/3 | -√32 | 12 | -√3 | -2√33 | 2 | -√33 |
| 315° | 7π/4 | -√22 | √22 | -1 | -√2 | √2 | -1 |
| 330° | 11π/6 | -12 | √32 | -√33 | -2 | 2√33 | -√3 |
| 360° | 2π | 0 | 1 | 0 | Undefined | 1 | Undefined |
Trigonometric Function Signs by Quadrant (ASTC Cheat Sheet)
sin, cos, tan, csc, sec, cot ratios are all positive.
Only sin and csc are positive. cos, tan, sec, cot are negative (-).
Only tan and cot are positive. sin, cos, csc, sec are negative (-).
Only cos and sec are positive. sin, tan, csc, cot are negative (-).
Why Use Our Trig Values Table?
Complete 0°–360° Reference Table
Displays exact fractional and radical values for all 6 trig functions (sin, cos, tan, csc, sec, cot) at every standard angle from 0° to 360° in one scrollable table.
Custom Angle Solver
Input any angle in degrees or radians and instantly obtain exact expressions (for standard angles) or high-precision 6-decimal approximations (for custom angles).
Interactive Unit Circle Visualizer
A live SVG unit circle animates the vector, cosine projection, and sine projection for any entered angle, making abstract ratios visually intuitive.
ASTC Quadrant Cheat Sheet
Includes a clear All-Students-Take-Calculus quadrant guide that shows which trig functions are positive or negative in each of the four quadrants.
Instant Exact Fraction Rendering
Standard angle values are displayed as formatted inline fractions (e.g., √3/2) with proper numerator-over-denominator layout — not plain text strings.
100% Private & Client-Side
Every calculation, table rendering, and SVG animation runs entirely in your browser. No data is transmitted to servers — your calculations stay private.
Common Use Cases for Trig Values Table
Students & Homework
Quickly look up sin, cos, or tan for standard angles to verify homework answers, check exam preparation, and build intuitive memory for unit circle values.
Exam Prep & Memorization
Use the color-highlighted reference table to memorize exact values like sin 30° = 1/2, cos 45° = √2/2, and tan 60° = √3 with clearly formatted fractions.
Engineering Calculations
Mechanical and electrical engineers use exact trig values when computing forces, signal waveforms, vector components, and rotational kinematics.
Physics & Wave Analysis
Physicists analyzing wave equations, oscillations, or projectile motion need precise sin/cos values to calculate amplitudes, frequencies, and displacement.
Computer Graphics & Game Dev
Game developers and 3D artists rely on exact trig ratios for rotation matrices, camera projections, and smooth animation interpolation at key angles.
Architecture & Surveying
Surveyors and architects use trig ratios to calculate roof pitches, staircase angles, load-bearing forces, and triangulation measurements for blueprints.
Understanding Trigonometric Values & the Unit Circle
What Are Trigonometric Functions?
Trigonometric functions are mathematical relationships between angles and the ratios of the sides of a right triangle. The six primary trig functions are: sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot). Given an angle θ in a right triangle with sides labeled as opposite (opp), adjacent (adj), and hypotenuse (hyp):
- sin θ = opposite / hypotenuse
- cos θ = adjacent / hypotenuse
- tan θ = opposite / adjacent = sin θ / cos θ
- csc θ = 1 / sin θ (hypotenuse / opposite)
- sec θ = 1 / cos θ (hypotenuse / adjacent)
- cot θ = 1 / tan θ (adjacent / opposite)
The Unit Circle and Standard Angles
The unit circle is a circle of radius 1 centered at the origin of a coordinate plane. For any angle θ, a point on the unit circle has coordinates (cos θ, sin θ). This geometric definition extends trigonometry beyond right triangles to all real-numbered angles (including negative and beyond 360°). The standard angles most commonly memorized are multiples of 30° (π/6) and 45° (π/4), derived from two special right triangles:
- 45°-45°-90° Triangle: sides in ratio 1 : 1 : √2. Yields sin 45° = cos 45° = √2/2.
- 30°-60°-90° Triangle: sides in ratio 1 : √3 : 2. Yields sin 30° = 1/2, cos 30° = √3/2, sin 60° = √3/2, cos 60° = 1/2.
Degrees vs. Radians
Angles can be measured in degrees (a full circle = 360°) or radians (a full circle = 2π radians). Radians are the natural unit for trigonometry in calculus and advanced mathematics because derivatives of trig functions are simpler (d/dx(sin x) = cos x only holds in radians). The conversion formula is:
radians = degrees × (π / 180) | degrees = radians × (180 / π)
For example, 180° equals π radians, 90° equals π/2 radians, and 45° equals π/4 radians.
Reference Angles and Quadrant Signs
A reference angle is the positive acute angle (0° to 90°) between the terminal side of any angle and the x-axis. All trig values for an angle can be computed from its reference angle, with the sign determined by which quadrant the angle lies in (using the ASTC rule):
- Quadrant I (0°–90°): All functions positive.
- Quadrant II (90°–180°): Only sin and csc are positive.
- Quadrant III (180°–270°): Only tan and cot are positive.
- Quadrant IV (270°–360°): Only cos and sec are positive.
For example, sin 150° = sin(180° − 30°) = sin 30° = 1/2 (Quadrant II, sin positive). And cos 150° = −cos 30° = −√3/2 (negative in Q II).
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Frequently Asked Questions About Trig Values Table
The Trig Values Table is a comprehensive mathematical reference chart that lists the exact values of the six primary trigonometric functions (sine, cosine, tangent, cosecant, secant, and cotangent) for standard angles in both degrees (from 0° to 360°) and radians.
Exact values are derived from special right triangles: the 45°-45°-90° triangle (sides ratio 1:1:√2) and the 30°-60°-90° triangle (sides ratio 1:√3:2). By applying the definitions of trigonometric ratios (opposite/hypotenuse, adjacent/hypotenuse, etc.) to these triangles, exact values like 1/2, √2/2, and √3/2 are calculated.
Standard angles are multiples of 30° and 45° around the unit circle. The primary standard angles in the first quadrant are 0° (0 rad), 30° (π/6 rad), 45° (π/4 rad), 60° (π/3 rad), and 90° (π/2 rad). Other standard angles in quadrants II, III, and IV share the same reference angles.
To convert degrees to radians, multiply the angle in degrees by π/180. For example, 180° × (π/180) = π radians, and 30° × (π/180) = π/6 radians. To convert radians back to degrees, multiply by 180/π.
Tangent is defined as the ratio of sine to cosine (tan θ = sin θ / cos θ). At 90 degrees, sin(90°) = 1 and cos(90°) = 0. Since division by zero is mathematically undefined, tangent is undefined at 90° (representing a vertical asymptote on the tangent graph). Similarly, cot is undefined at 0° and 180°, csc at 0° and 180°, and sec at 90° and 270°.
The ASTC rule ("All Students Take Calculus") helps remember which functions are positive in each quadrant: Quadrant I (A) — All functions are positive; Quadrant II (S) — Sine (and cosecant) are positive; Quadrant III (T) — Tangent (and cotangent) are positive; Quadrant IV (C) — Cosine (and secant) are positive.
Yes. Our custom angle solver allows you to input any decimal angle in degrees or radians. It will instantly calculate the exact value if it is a standard multiple, or provide a highly accurate decimal approximation alongside its reference angle, quadrant, and algebraic signs.
Absolutely. All trigonometric calculations, table formatting, and SVG unit circle rendering are executed entirely client-side inside your browser. No input values are sent to external servers, ensuring 100% data privacy.