About this calculator
The Tangent Calculator finds tan(x) in degrees or radians and highlights undefined results where cosine is zero. It is useful for gradients, angles of elevation, right-triangle problems, and checking tangent values before using them in further working.
tangent calculator method
In a right triangle, tangent is the opposite side divided by the adjacent side. On the unit circle, tangent is sine divided by cosine, which is why it is undefined when cosine is zero.
- tan(theta) = opposite / adjacent
- tan(theta) = sin(theta) / cos(theta)
- radians = degrees x pi / 180
How to use the tangent calculator
- Enter the angle.
- Choose degrees or radians.
- Read the tangent result.
- Check whether the angle is close to 90 degrees or 270 degrees.
- Use the sine and cosine context values to understand the result.
- Round the final answer to the required precision.
Worked examples
Tangent of 45 degrees
Input: 45 degrees
Calculation: tan(45 degrees)
Result: 1
Angle of elevation
Input: Opposite 3, adjacent 4
Calculation: tan(theta) = 3 / 4
Result: theta is about 36.87 degrees
Undefined tangent values
Tangent becomes undefined when the adjacent side or cosine value is zero. In degree measure this happens at 90 degrees, 270 degrees, and coterminal angles.
Tangent and gradient
Tangent is closely linked to slope. A larger tangent value means a steeper angle, while a tangent of 1 corresponds to a 45-degree angle.
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
- Cosine Calculator