Trigonometry Calculator
Enter an angle to see all six trigonometric functions, with exact values such as √3/2 for the standard angles. Or switch to the inverse and find the angles that give a value, or the angle of a right-angled triangle from two sides.
Worked examples
A standard angle
30 degrees
sin 1/2, cos √3/2, tan √3/3
Decimals 0.5, 0.866025 and 0.577350.
All angles for a sine
sin⁻¹ of 0.5
30 and 150 degrees
Both have a sine of 0.5.
About Trigonometry Calculator
The trigonometric functions link an angle to a ratio of sides. In a right-angled triangle, the sine of an angle is the opposite side over the hypotenuse, the cosine is the adjacent over the hypotenuse, and the tangent is the opposite over the adjacent. Their reciprocals are the cosecant, secant and cotangent. For angles outside 0 to 90 degrees the functions come from a point going round a circle of radius 1, so they can be negative. Some angles give exact values: the sine of 30 degrees is exactly 1/2, of 45 degrees is √2/2 and of 60 degrees is √3/2.
This calculator shows all six functions for any angle in degrees or radians, with the exact value beside the decimal for the standard angles and every angle that shares a reference angle with them. Where a function is undefined, such as the tangent of 90 degrees, it says so. Switch to the inverse mode to go the other way: enter a sine, cosine or tangent value, or the opposite and adjacent sides, and get the angle in degrees and radians together with every angle from 0 to 360 degrees that gives the same value.
How to use Trigonometry Calculator
- Choose whether to find the functions of an angle or to find an angle.
- For an angle, type it in and choose degrees or radians. You can type pi/6 and similar.
- For the inverse, choose sin⁻¹, cos⁻¹, tan⁻¹ or two sides, and enter the value.
- Read the table of results, or the principal angle and the list of all angles up to 360 degrees.
Common uses
- Right-angled triangle problems at GCSE and A level
- Finding angles of slopes, ramps and roofs
- Solving trigonometric equations over 0 to 360 degrees
- Checking exact values for 30, 45 and 60 degrees
Frequently asked questions
How do I remember sine, cosine and tangent?
SOH CAH TOA: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse and tangent is opposite over adjacent.
Why is the tangent of 90 degrees undefined?
The tangent is sine divided by cosine, and the cosine of 90 degrees is zero. Dividing by zero has no answer, so the page says undefined.
Why does inverse sine give two angles?
The sine is positive in two quadrants, so an angle and 180 minus that angle share a value. A calculator only gives the principal one, so the page lists both. Cosine and tangent have two between 0 and 360 as well.
Degrees or radians?
Use degrees for everyday angles and school problems, and radians in calculus and most science. Select the unit that matches your problem.
What is a reference angle?
It is the acute angle between the line and the x axis. Knowing it and the quadrant is enough to find any sine, cosine or tangent from the first-quadrant values.