Complementary angle identities

Learning Objectives Define complementary angles and identify trigonometric cofunction pairs. Recall and state the six complementary angle identities (cofunction identities) in both degrees and radians. Apply complementary angle identities to simplify complex trigonometric expressions. Solve trigonometric equations by utilizing the relationship between cofunctions. Prove more complex trigonometric identities by incorporating complementary angle identities. Evaluate trigonometric functions of angles without a calculator by converting them to their cofunction of a known acute angle. Ever wondered why sin(30°) is the exact same as cos(60°)? 🤔 This isn't a coincidence; it's a fundamental property of right-angled triangles that unlocks powerful shortcuts! This tutorial...

TermDefinitionExample Complementary AnglesTwo angles are complementary if their sum is 90° (or π/2 radians). In a right-angled triangle, the two acute angles are always complementary.30° and 60° are complementary angles because 30° + 60° = 90°. Similarly, π/6 and π/3 are complementary because π/6 + π/3 = π/2. Trigonometric IdentityAn equation involving trigonometric functions that holds true for all values of the variable for which both sides of the equation are defined.The Pythagorean identity, sin²(θ) + cos²(θ) = 1, is true for any angle θ. CofunctionsPairs of trigonometric functions where the prefix 'co-' indicates a complementary relationship. The value of a trig function of an angle is equal to the value of its cofunction at the complementary angle.Sine and Cosine are cofun...

Sine and Cosine Cofunction Identity sin(π/2 - θ) = cos(θ) and cos(π/2 - θ) = sin(θ) The sine of an angle is the cosine of its complement, and vice versa. Use this to switch between sine and cosine functions in an expression or equation. Tangent and Cotangent Cofunction Identity tan(π/2 - θ) = cot(θ) and cot(π/2 - θ) = tan(θ) The tangent of an angle is the cotangent of its complement, and vice versa. This is useful for simplifying expressions involving tangent and cotangent. Secant and Cosecant Cofunction Identity sec(π/2 - θ) = csc(θ) and csc(π/2 - θ) = sec(θ) The secant of an angle is the cosecant of its complement, and vice versa. This applies the same principle to the reciprocal trigonometric functions.