About this calculator
The Trigonometry Calculator works out sine, cosine, tangent, arcsine, arccosine, and arctangent values in degrees or radians. It is useful for students checking GCSE or A-Level work, teachers creating examples, and anyone who needs a quick way to connect angles, ratios, and the unit circle.
trigonometry calculator method
For sine, cosine, and tangent, the calculator converts the angle to radians when needed, then applies the standard trig function. For inverse functions, it works backwards from a ratio to the principal angle.
- radians = degrees x pi / 180
- sin(theta), cos(theta), tan(theta) use theta in radians
- arcsin(value), arccos(value), arctan(value) return a principal angle
How to use the trigonometry calculator
- Choose sin, cos, tan, arcsin, arccos, or arctan.
- Enter the angle or trig ratio.
- Select degrees or radians for the input or output unit.
- Review the main result.
- Compare the degree and radian form shown underneath.
- Use the common values table to check familiar angles.
- Use the unit circle visual to connect sine with y and cosine with x.
Worked examples
Sine of 30 degrees
Input: Function sin, angle 30 degrees
Calculation: sin(30 degrees) = sin(pi / 6)
Result: 0.5
Cosine of 60 degrees
Input: Function cos, angle 60 degrees
Calculation: cos(60 degrees) = cos(pi / 3)
Result: 0.5
Inverse tangent
Input: Function arctan, value 1
Calculation: arctan(1)
Result: 45 degrees, or pi / 4 radians
Trig functions in plain English
Sine, cosine, and tangent describe relationships between an angle and a ratio. In a right triangle, those ratios compare side lengths. On the unit circle, sine is the y-coordinate, cosine is the x-coordinate, and tangent is the ratio of sine to cosine.
The inverse functions go the other way. Instead of asking for the ratio from an angle, they ask for the angle that produces a ratio.
Unit circle values
The common angles 0, 30, 45, 60, and 90 degrees are worth learning because they appear often in exams and examples. The calculator includes them as a quick check against the live result.
Common mistakes to avoid
- Mixing degrees and radians
- Most wrong trigonometry answers come from using the wrong angle unit. Check whether the question, calculator, or exam setting is using degrees or radians before comparing results.
- Rounding too early
- Keep extra decimal places during working, then round the final answer. Rounding sine, cosine, or tangent too early can noticeably change a side length or angle.
- Using trig on a non-right triangle
- SOHCAHTOA only applies directly to right-angled triangles. Other triangles may need the sine rule, cosine rule, or a split into right triangles.
Edge cases
- Tangent is undefined where cosine is zero, such as 90 degrees and 270 degrees.
- Inverse sine and inverse cosine only accept inputs from -1 to 1.
- Angles that differ by 360 degrees can have the same sine, cosine, and tangent values.
- A calculated triangle side should not be negative. Recheck the selected side labels if that happens.
Limitations
This calculator is for educational maths support. It uses standard trigonometric formulas and JavaScript Math functions, so results are numerical approximations. For coursework, exams, engineering, surveying, or safety-critical work, follow the required method, units, precision, and marking guidance.
Frequently asked questions
Should I use degrees or radians?
Use the unit given in the question. GCSE-style triangle questions usually use degrees. A-Level maths, calculus, circular motion, and many scientific formulas often use radians.
What does SOHCAHTOA mean?
SOHCAHTOA is a memory aid: sine equals opposite over hypotenuse, cosine equals adjacent over hypotenuse, and tangent equals opposite over adjacent.
Why is tan 90 degrees undefined?
Tangent is sine divided by cosine. At 90 degrees, cosine is zero, so the division is not defined.
Why do inverse trig calculators sometimes give only one angle?
Inverse trig functions return a principal value. Some trig equations have multiple valid angles over a larger interval, so the calculator result may be one of several possible angles.
Can I use these calculators for GCSE and A-Level revision?
Yes, they are useful for checking working and building confidence. Always practise writing the full method because exam marks often depend on the steps, not just the final number.
Related calculators
- SOHCAHTOA Calculator
- Sine Calculator
- Degrees to Radians Calculator