How this instrument works
Sine, cosine, and tangent are the three core ratios built from a right triangle's sides relative to one of its acute angles: sine is the opposite side over the hypotenuse, cosine is the adjacent side over the hypotenuse, and tangent is opposite over adjacent, which also equals sine divided by cosine. All three track the same angle, phrased through a different pair of sides, and each swings between fixed bounds as that angle sweeps around a full circle.
Pick a function from the dropdown first, then enter the angle: the sheet branches internally on that choice and computes only the ratio requested, the same selector-and-branch pattern used elsewhere on this site wherever a calculator offers a handful of related modes rather than one fixed formula. A sibling sheet returns sine, cosine, and tangent together for a single angle in one pass; this page is built for the narrower moment when only one of the three is actually needed and displaying the other two would just clutter the result.
Degrees are the default unit for the angle field, though radians and turns both remain available whenever that suits the source numbers better. Switching units never changes the underlying math, since the angle gets converted before any ratio is evaluated, so entering 30 degrees or its radian equivalent, roughly 0.5236, produces an identical answer either way.
- Pick a function from the dropdown: sine, cosine, or tangent.
- Enter the Angle, choosing degrees, radians, or turns as the unit.
- Read Result, the value of whichever function was selected.
- Switch the dropdown to compare a different function at the same angle.
Worked example — the same dropdown, three separate picks
Select sine and enter 30°: Result = sin(30°) = 0.5. That half comes straight from the classic 30-60-90 right triangle, where the side opposite the 30° angle measures exactly half the hypotenuse.
Switch the dropdown to cosine and enter 60° instead: Result = cos(60°) = 0.5 again, since cosine of an angle equals sine of its complement, and 90° minus 60° is 30°. Switch once more to tangent and enter 45°: Result = tan(45°) = 1.0, the one angle where sine and cosine come out equal, making their ratio exactly one.
Questions
How is this different from a calculator that gives sine, cosine, and tangent together?
This page keeps a single dropdown and evaluates only the function picked, so the output is one number instead of three. A sibling sheet reports all three ratios at once for a given angle; reach for that version when every ratio is wanted, and reach for this one when only sine, only cosine, or only tangent is actually needed.
Why do sine of 30° and cosine of 60° give the same result?
Because 30° and 60° are complementary, adding to 90°, and cosine of an angle always equals sine of its complement. Sine of 30° and cosine of 60° both come out to 0.5, a pattern that holds for any pair of angles adding to a right angle, not just this one.
Why does tangent of 45° come out to exactly 1?
At 45°, sine and cosine equal each other, both near 0.7071, and tangent is defined as sine divided by cosine. Dividing a number by itself gives 1, so tangent of 45° lands on exactly 1.0 with no rounding involved anywhere in the calculation.
What angle units can I enter?
Degrees, radians, or turns; pick whichever matches the source data using the unit selector beside the Angle field. The sheet converts to radians internally before evaluating whichever function the dropdown has selected, so switching units never changes the reported Result.
Can tangent ever be undefined for an angle I enter?
Yes, at 90°, 270°, and any angle where cosine equals zero, since tangent equals sine over cosine and dividing by zero has no defined value. Entries near those angles return extremely large numbers rather than a clean result, a sign of approaching that boundary rather than an error in the sheet.