The right triangle method converts between inverse trig functions. If sin^(-1)(x) = theta, draw a right triangle with opposite = x, hypotenuse = 1, adjacent = sqrt(1-). Then: cos(theta) = sqrt(1-), tan(theta) = (1-), etc. So sin^(-1)(x) = tan^(-1)(x/sqrt(1-)) = cos^(-1)(sqrt(1-)) for x in [0, 1]. For negative x, use parity: sin^(-1)(-x) = -sin^(-1)(x) then convert the positive part. Similarly, if tan^(-1)(x) = theta: sin(theta) = (1+), cos(theta) = 1/sqrt(1+). These conversions are essential when different inverse trig functions appear in the same equation.
Part of TRIG-02 — Inverse Trigonometric Functions
Converting Between Inverse Trig Functions
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