Name the sides from the chosen angle
In a right triangle, opposite and adjacent depend on which acute angle you choose. The hypotenuse always remains opposite the right angle. Sine uses opposite/hypotenuse; cosine uses adjacent/hypotenuse.
Tangent is opposite/adjacent, equivalently sine divided by cosine. Ratios have no length units when both measurements use the same unit.
Angles may be degrees or radians
Use DEG for an input such as 60 degrees, and RAD for an input such as π/3. Both describe the same angle. The number 60 entered in radians describes something entirely different.
Beyond acute right-triangle angles, the unit circle defines the functions for positive and negative rotations. Signs change by quadrant; a negative output can therefore be valid.
Watch reciprocal and pole behavior
Tangent and secant are undefined where cosine is zero. Cosecant and cotangent are undefined where sine is zero. Close to a pole, a large finite value can be mathematically valid.
The calculator distinguishes an exact degree pole from a nearby valid angle. For very large angle inputs, numerical precision still limits how much detail can be recovered.
LET’S WORK IT THROUGH
Find sin(30°), cos(60°) and tan(45°).
- Select degrees for these inputs.
- sin(30°) = 1/2 and cos(60°) = 1/2.
- tan(45°) = 1 because opposite and adjacent legs are equal.
THE ANSWER0.5, 0.5 and 1 respectively.
YOUR TURN
A small check for understanding.
Why is tan(90°) undefined?
Reveal the answer
Its cosine denominator is zero; division by zero is undefined.
Now try your own numbers.
The trigonometry calculator includes input guidance and the limits of its supported calculations. Use it alongside the method above.
Open Trigonometry calculator ↗A note on precision: preserve exact fractions where possible and round numerical results at the end. Found an unclear step? Prepare a correction report.