TQR_F07 - (Copyrighted by B. A. Forrest)...

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Unformatted text preview: (Copyrighted by B. A. Forrest) Email:bforrest@sympatico.ca Trigonometry Quick Reference Right Triangle Trigonometry sin θ = opposite hypotenuse cos θ = adjacent hypotenuse tan θ = opposite adjacent csc θ = 1 sin θ sec θ = 1 cos θ cot θ = 1 tan θ Radians π Definition of Sine and Cosine radians = 1 rad = 180◦ 180◦ π For any θ, cos θ and sin θ are defined to be the x− and y − coordinates of the point P on the unit circle such that the radius OP makes an angle of θ radians with the positive x− axis measured counter-clockwise. The Unit Circle Properties of the Sine and Cosine Functions Pythagorean Identity cos2 θ + sin2 θ = 1 Periodicity cos(θ ± 2π ) = cos θ sin(θ ± 2π ) = sin θ Range −1 ≤ cos θ ≤ 1 −1 ≤ sin θ ≤ 1 Symmetry cos(−θ) = cos θ sin(−θ) = − sin θ 1 Trigonometric Identities Sum and Difference Identities Complementary Angle Identities cos( π − A) = sin A 2 sin( π − A) = cos A 2 Double-Angle Identities cos 2A = cos2 A − sin2 A sin 2A = 2 sin A cos A Half-Angle Identities cos2 θ = 1+cos 2θ 2 sin2 θ = 1−cos 2θ 2 Other cos(A + B ) = cos A cos B − sin A sin B cos(A − B ) = cos A cos B + sin A sin B sin(A + B ) = sin A cos B + cos A sin B sin(A − B ) = sin A cos B − cos A sin B 1 + tan2 A = sec2 A Trigonometry Graphs and their Properties Inverse Trigonometric Functions You Need to Know 2 ...
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This note was uploaded on 10/21/2010 for the course MATH 147 taught by Professor Wolzcuk during the Fall '09 term at Waterloo.

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