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- Finds sin, cos, tan, csc, sec and cot of any angle.
- Accepts degrees, radians or multiples of π (such as π/3).
- Shows exact values like √3/2 for special angles, plus decimals.
- Also does inverse trig (arcsin, arccos, arctan) and gives the quadrant and reference angle.
How to use the trig calculator
Choose a mode
Pick sin, cos, tan of an angle, or inverse trig to find an angle from a ratio.
Enter the angle
Type the angle and choose degrees, radians or multiples of π. For π/3, choose multiples of π and type 0.3333 or 1/3 as 0.333333.
Read all six functions
sin, cos, tan and their reciprocals appear, with exact forms for special angles.
Check the angle details
See the angle in degrees and radians, its quadrant, coterminal angle and reference angle.
How the trig functions work
Right-triangle definitions
sin θ = opposite ÷ hypotenuse
cos θ = adjacent ÷ hypotenuse
tan θ = opposite ÷ adjacent = sin θ ÷ cos θ
On the unit circle, cos θ is the x-coordinate and sin θ is the y-coordinate of the point at angle θ.
Reciprocal functions and conversion
csc θ = 1/sin θ, sec θ = 1/cos θ, cot θ = 1/tan θ
radians = degrees × π ÷ 180
A function is undefined where its denominator is 0, for example tan 90°.
Special angles (unit circle values)
Exact values worth memorising.
- sin 30°, cos 60° 1/2
- sin 45°, cos 45° √2/2 ≈ 0.707107
- sin 60°, cos 30° √3/2 ≈ 0.866025
- tan 30° √3/3 ≈ 0.57735
- tan 45° 1
- tan 60° √3 ≈ 1.732051
- tan 90° undefined
The same values repeat in every quadrant, only the sign changes.
Example: sin, cos and tan of π/3
π/3 radians is 60°.
- sin(π/3) √3/2
- cos(π/3) 1/2
- tan(π/3) √3
For a non-special angle such as 37°, the calculator gives decimals: sin 37° ≈ 0.601815.
Example: inverse tangent
Find the angle whose tangent is 0.75 (a 3-4-5 triangle).
- arctan(0.75) 36.8699°
- arcsin(0.75) 48.5904°
- arccos(0.75) 41.4096°
Inverse functions give one principal angle. Other angles with the same ratio also exist.
Where a trig calculator helps
Trigonometry homework
Check unit circle values and exact forms without a table.
Physics and engineering
Split forces and velocities into x and y parts using sin and cos.
Building and DIY
Work out roof angles, ramp slopes and cut angles.
Navigation and games
Turn headings and directions into coordinates.
Solve a triangle’s missing side with the Pythagorean theorem calculator, find an angle from two points with the slope calculator, or convert exact answers with the square root calculator.
Trig calculator FAQ
What is sin, cos and tan?
They are ratios of the sides of a right triangle: sin is opposite over hypotenuse, cos is adjacent over hypotenuse, and tan is opposite over adjacent.
How do I enter π/3?
Choose “Multiples of π” and type 1/3 as a decimal (0.333333), or choose degrees and type 60.
Why is tan 90° undefined?
tan = sin ÷ cos, and cos 90° = 0. Dividing by 0 is undefined.
What is a reference angle?
It is the acute angle between the terminal side of your angle and the x-axis. It tells you which special-angle values to use.
Should my calculator be in degrees or radians?
Use degrees when the angle has a degree sign (°) and radians when it is written with π or has no unit in calculus. This calculator lets you pick either.
What does arctan give me?
arctan (tan⁻¹) gives the angle between −90° and 90° whose tangent equals your value.