Given a trig ratio, find the angle using arcsin, arccos, or arctan. See domain restrictions, the answer in degrees and radians, and the reference angle on a unit circle.
θ = arcsin(x) ⟺ sin(θ) = x, θ ∈ [−90°, 90°]
θ = arccos(x) ⟺ cos(θ) = x, θ ∈ [0°, 180°]
θ = arctan(x) ⟺ tan(θ) = x, θ ∈ (−90°, 90°)
The inverse trig functions "undo" sin, cos, and tan — they return the angle whose ratio equals the input. Because trig functions are periodic, the inverse functions have restricted ranges to ensure unique outputs.
The reference angle is the acute angle (0°–90°) between the terminal side and the x-axis. It tells you the magnitude, while the quadrant determines the sign.
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