About this calculator
The Cosine Calculator finds cos(x) for an angle in degrees or radians and displays sine and tangent alongside the result. It is useful for adjacent-side right-triangle calculations, unit circle checks, vectors, and angle-based geometry work.
cosine calculator method
In a right triangle, cosine is the adjacent side divided by the hypotenuse. The calculator converts degree inputs into radians where needed, then applies the cosine function.
- cos(theta) = adjacent / hypotenuse
- radians = degrees x pi / 180
- cos(theta) is the x-coordinate on the unit circle
How to use the cosine calculator
- Enter the angle value.
- Choose whether the angle is in degrees or radians.
- Read the cosine result.
- Check the accompanying sine and tangent values.
- Compare common values such as 0, 30, 45, 60, and 90 degrees.
- Round only after completing the main working.
Worked examples
Cosine of 60 degrees
Input: 60 degrees
Calculation: cos(60 degrees)
Result: 0.5
Adjacent side
Input: Hypotenuse 10, angle 60 degrees
Calculation: adjacent = 10 x cos(60 degrees)
Result: 5
Cosine on the unit circle
On the unit circle, cosine is the horizontal coordinate of the point reached by the angle. This is why cos(0 degrees) is 1 and cos(90 degrees) is 0.
Cosine range
Cosine values stay between -1 and 1. They are positive on the right side of the unit circle and negative on the left side.
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
- Trigonometry Calculator
- Sine Calculator
- Tangent Calculator