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Trigonometric identities and equations

Define reciprocal trig ratios, apply Pythagorean and complementary identities, and prove and solve trig equations.

Functions · MAV-11-05

Sub-topics

Reciprocal trig ratios

Define secant, cosecant and cotangent; evaluate them for standard angles using exact values; apply reciprocal identities to simplify trigonometric expressions; prove simple identities involving reciprocal ratios.

Trigonometric identities

Verify the Pythagorean identity; use it to find unknown trig ratios given one ratio and the quadrant; apply the identities

1 + \tan^2\theta = \sec^2\theta

1 + \cot^2\theta = \csc^2\theta

; use complementary angle identities; prove two-step identities by expressing everything in terms of

\sin\theta

\cos\theta

Trigonometric equations

Solve trigonometric equations for all solutions in a given domain, including equations requiring Pythagorean identity substitution and equations that reduce to a quadratic in a trigonometric function.