Trig Ratios Calculator
Enter an angle in degrees or radians and get its sine, cosine, tangent, and the reciprocal ratios cosecant, secant and cotangent.
How it works
sin, cos, tan of θ · csc = 1/sin · sec = 1/cos · cot = cos/sin
The three primary trig ratios describe a right triangle: sine is opposite over hypotenuse, cosine is adjacent over hypotenuse, and tangent is opposite over adjacent (equivalently sin/cos). The reciprocal ratios cosecant, secant and cotangent are simply 1/sin, 1/cos and 1/tan. Tangent and secant are undefined wherever cosine is zero (90°, 270°, …), and cosecant and cotangent are undefined where sine is zero (0°, 180°, …).
Worked example
At 30°: sin 30° = 0.5, cos 30° = 0.8660, tan 30° = 0.5774. The reciprocals are csc = 2, sec = 1.1547 and cot = 1.7321.
Sources: Trigonometric functions — Wikipedia
Frequently asked questions
What does SOH-CAH-TOA mean?
It is a memory aid: Sine = Opposite/Hypotenuse, Cosine = Adjacent/Hypotenuse, Tangent = Opposite/Adjacent. It links each ratio to the sides of a right triangle.
Why is tan 90° undefined?
Tangent equals sin/cos, and cos 90° = 0. Dividing by zero is undefined, so tangent has no finite value at 90° (and every 180° after it). This calculator reports "undefined" there rather than a bogus huge number.
Should I use degrees or radians?
Either — pick the unit that matches your problem. Everyday geometry usually uses degrees; calculus and physics usually use radians. The calculator converts internally so the ratios are correct in both.
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This calculator is for educational purposes. Double-check important results before acting on them.