Complementary Angles

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Two acute angles are said to be complementary if their sum is 90°. Examples: 1. 30° and 60° are complementary (30° + 60° = 90°) 2. 45° and 45° are complementary (45° + 45° = 90°) 3. θ and (90° - θ) a

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Complement of 35° = 90° - 35° = 55° General rule: For any angle θ, its complement = (90° - θ)

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sin θ = cos(90° - θ) This means: The sine of an angle equals the cosine of its complement. Example: sin 30° = cos 60° = 1/2

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cos θ = sin(90° - θ) This means: The cosine of an angle equals the sine of its complement. Example: cos 30° = sin 60° = √3/2

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sin 40°/cos 50° = sin 40°/cos(90° - 40°) = sin 40°/sin 40° = 1 Since cos 50° = cos(90° - 40°) = sin 40°

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tan θ = cot(90° - θ) This means: The tangent of an angle equals the cotangent of its complement. Example: tan 45° = cot 45° = 1

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cot θ = tan(90° - θ) This means: The cotangent of an angle equals the tangent of its complement. Example: cot 30° = tan 60° = √3

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tan 25°/cot 65° = tan 25°/cot(90° - 25°) = tan 25°/tan 25° = 1 Since cot 65° = cot(90° - 25°) = tan 25°