What are inverse trigonometric functions?
Inverse sine, cosine, and tangent (written sin⁻¹, cos⁻¹, tan⁻¹) turn a ratio of sides back into the angle that produced it. They undo the ordinary sine, cosine, and tangent.
// maths › Right-Angle Trigonometry
Find an angle
Find an unknown acute angle in a right triangle from two known sides using the inverse sine, cosine, or tangent, with a diagram that draws and labels the angle arc once it is solved.
θ = sin⁻¹(O/H) · cos⁻¹(A/H) · tan⁻¹(O/A)
Angle unit
Frequently asked questions
Which inverse function do I use?
Choose by the sides you know: opposite and hypotenuse use inverse sine, adjacent and hypotenuse use inverse cosine, and opposite and adjacent use inverse tangent.
Can you show a worked example?
If the opposite is 5 and the hypotenuse is 10, then sin θ = 5/10 = 0.5, so θ = sin⁻¹(0.5) = 30°. In radians that same angle is π/6 ≈ 0.5236 rad; switch the toggle and the answer is shown that way.
Where is the inverse button on a calculator?
It is usually the second function above the sin, cos, and tan keys, reached with a shift or 2nd key. Make sure the calculator is set to the same mode — degrees or radians — as the answer you want.
Where is this used in real life?
Engineers find slope and ramp angles, pilots and sailors compute headings, construction crews check pitch and incline, and physicists and game developers work out launch and reflection angles.