How to Find Exact Value of Trig Functions?

Use special right triangles: 45°-45°-90° and 30°-60°-90°

Memorize exact trig values for common angles: 0°, 30°, 45°, 60°, 90°

Use the unit circle to read exact values of sine, cosine, and tangent

Apply reference angles to find values in any quadrant

Determine the sign of the trig function based on the quadrant

Use reciprocal identities for cosecant, secant, and cotangent

Use Pythagorean identities to find missing exact values

Use angle sum and difference identities for nonstandard angles

Use double-angle and half-angle identities when needed

Simplify radicals and fractions to exact form

Rationalize denominators if required

Check for undefined values such as tangent at 90° and cosine at 90° in reciprocal forms

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