Sin Cos Tan Calculator
This sin cos tan calculator gives the sine, cosine and tangent of an angle in degrees, radians or gradians – or finds the angle from a given value. For 30° it shows sin = 0.5, cos = 0.866025 and tan = 0.57735, and for standard angles the exact value as well.
Example: What do you want to calculate: Sine, cosine, tangent of an angle · Angle 30 · Unit: Degrees (°) → Result: sin 30° = 0.5. Source: Wikipedia – Trigonometric functions (definitions, periodicity, inverse functions). Updated: .
How it is calculated
How to calculate sine, cosine and tangent
In a right triangle, for an acute angle α: sin α = opposite ÷ hypotenuse, cos α = adjacent ÷ hypotenuse and tan α = opposite ÷ adjacent. On the unit circle, cosine and sine are the x and y coordinates of the point at that angle; the tangent is sin ÷ cos.
Degrees, radians and gradians
A full circle is 360 degrees, 2π radians or 400 gradians. To convert: rad = degrees × π ÷ 180. Always set your calculator and this tool to the same unit, otherwise the results look wrong: sin 30 is 0.5 in degrees but −0.988 in radians.
Values worth knowing
- 0°: sin 0, cos 1, tan 0
- 30°: sin ½, cos √3⁄2, tan √3⁄3
- 45°: sin √2⁄2, cos √2⁄2, tan 1
- 60°: sin √3⁄2, cos ½, tan √3
- 90°: sin 1, cos 0, tan undefined
Finding an angle from a value
With arcsin, arccos and arctan (the inverse functions) you get the angle for a value. The calculator shows the principal value and the second solution between 0° and 360°: arcsin 0.5 = 30° and also 150°.
Honest limits
Output is rounded to eight decimals. Multiples of 90° are calculated exactly so that no floating-point noise such as 1.2e-16 appears. For complete triangles with sides and angles there is the triangle calculator.
Frequently asked questions
How do I calculate sin, cos and tan?
Enter the angle and its unit – the calculator shows sin, cos, tan plus cotangent, secant and cosecant. For 30° sin is 0.5.
How do I calculate the cosine of an angle?
Choose “Sine, cosine, tangent of an angle”, enter the angle with its unit and read the cos line. The cosine of 60° is 0.5 and the cosine of 30° is 0.866025; in a right triangle it is adjacent ÷ hypotenuse.
How do I convert degrees to radians?
Use rad = degrees × π ÷ 180. For example 180° equals π rad (3.14159) and 90° equals π⁄2 rad.
Why does my calculator give a different sine?
It is most likely set to radians (RAD) instead of degrees (DEG). Set both to the same unit.
How do I find an angle from its sine?
Use the inverse function arcsin: for sin α = 0.5, α = 30° (principal value) or 150°.
What is the tangent of 90 degrees?
It is undefined, because the cosine is 0 there and you would divide by zero.
Sources and legal basis
- Wikipedia – Trigonometric functions (definitions, periodicity, inverse functions)
- Wikipedia – Exact trigonometric values (special angles)
As of: · Editorial policy
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