Graphs of sine and cosine and inverse functions

The inverse functions sin⁻¹, cos⁻¹ and tan⁻¹ give an angle from a ratio. A calculator gives only one angle (between −90° and 90° for sin⁻¹ and tan⁻¹, between 0° and 180° for cos⁻¹), but a ratio usually belongs to two angles in [0°, 360°[. Method: (1) ignore the sign and find the acute reference angle; (2) use the sign of the ratio to find the two quadrants (All, Sin, Tan, Cos); (3) write the angle in each quadrant, 180° − α, 180° + α or 360° − α. For ramps: if a ramp rises h over a horizontal distance d, tan θ = h/d; if the ramp itself has length ℓ, sin θ = h/ℓ. Always draw a right triangle first.