Half Angle Calculator

This half angle calculator works out sin(x/2), cos(x/2) and tan(x/2) for any angle x, using the standard half angle identities from trigonometry. Enter your angle, select whether it is in degrees or radians, and the calculator instantly returns all three half-angle values, with sin(x/2) shown as the main result and cos(x/2) and tan(x/2) alongside it. The textbook half angle formulas write these functions as square roots of expressions involving cos x, and those square roots carry a plus or minus sign that depends on which quadrant the half angle falls in, which is a common source of errors when working by hand. This tool sidesteps that problem entirely by converting your angle to the actual half angle in radians and evaluating each function directly, so the sign is always correct without you needing to reason about quadrants. It is useful for trigonometry and calculus students checking exact values, working through the tangent half angle substitution used in integration, or simply verifying homework and exam answers quickly. Try it with 60 degrees to see the worked example reproduced: sin(30) = 0.5, cos(30) = 0.866025 and tan(30) = 0.577350. Results are rounded to six decimal places for display, and tan(x/2) is reported as undefined where cos(x/2) is zero.

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