Trigonometry Calculator: sin, cos, tan, cosec, sec, cot of Any Angle
Enter an angle in degrees or radians (π/6 and 2π/3 work too). You get all six trigonometric ratios, exact surd values for standard angles and a unit-circle picture.
- Nothing you type is stored
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sin θ
1/2 = 0.5
- cos θ
- √3/2 ≈ 0.866025
- tan θ
- √3/3 ≈ 0.57735
- In radians
- π/6 = 0.523599
- Quadrant · reference angle
- Q1 · 30°
Signs follow the quadrant: Q1 all +, Q2 sin/cosec +, Q3 tan/cot +, Q4 cos/sec +.
Show working
- θ = 30° = π/6 rad
- θ mod 360° = 30°, ref = 30°
- sin θ = 1/2 = 0.5, cos θ = √3/2 ≈ 0.866025
- tan θ = sin θ / cos θ = √3/3 ≈ 0.57735
- cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
All six ratios
| Ratio | Value |
|---|---|
| sin θ | 1/2 = 0.5 |
| cos θ | √3/2 ≈ 0.866025 |
| tan θ | √3/3 ≈ 0.57735 |
| cosec θ | 2 |
| sec θ | 2√3/3 ≈ 1.154701 |
| cot θ | √3 ≈ 1.732051 |
How to use
- Type the angle, e.g. 30, 135 or 2π/3.
- Choose degrees or radians.
- Read sin, cos, tan and the full table of six ratios.
Good to know
Exact values are shown for every multiple of 15°: for example sin 30° = 1/2, cos 45° = √2/2, tan 60° = √3 and sin 15° = (√6 − √2)/4. Other angles show decimals to 6 places.
Signs by quadrant (“All Students Take Coffee”): all ratios are positive in Q1, only sin and cosec in Q2, only tan and cot in Q3, only cos and sec in Q4. The reference angle is the acute angle to the x-axis.
Where a ratio is not defined, a dash (—) is shown: tan 90°, sec 90°, cosec 0° and cot 0° divide by zero.
Questions
What is sin 30°?
Exactly 1/2. cos 30° = √3/2 and tan 30° = 1/√3 = √3/3.
How do I enter radians?
Choose radians and type a number like 1.2, or an expression with π such as π/4 or 2π/3.
Why is tan 90° not defined?
tan θ = sin θ / cos θ, and cos 90° = 0, so it would mean dividing by zero.
What are cosec, sec and cot?
The reciprocals: cosec θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ.
Is my data stored or sent anywhere?
No. The calculation runs entirely in your browser; nothing you type leaves your device.