Part of TRIG-02 — Inverse Trigonometric Functions

Converting Between Inverse Trig Functions

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Use a right triangle: if sin^(-1)(x) = theta, then sin(theta) = x, so the opposite side is x and hypotenuse is 1, adjacent = sqrt(1-x2x^2). Therefore: cos(theta) = sqrt(1-x2x^2), tan(theta) = xsqrt\frac{x}{sqrt}(1-x2x^2). This gives: sin^(-1)(x) = cos^(-1)(sqrt(1-x2x^2)) = tan^(-1)(x/sqrt(1-x2x^2)) for x >= 0.

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