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Algebra 2 Tuesday, April 07, 2009 Section 12.2: Trigonometric Functions of Acute Angles e s nu p hy te n o opposite side θ adjacent side Trigonometric Functions: opposite sin θ = hypontenuse csc θ = cos θ = adjacent hypontenuse sec θ = tan θ = opposite sin θ = adjacent cos θ cot θ = hypontenuse opposite hypontenuse adjacent adjacent = cos θ opposite sin θ 1 Algebra 2 Tuesday, April 07, 2009 Section 12.2: Trigonometric Functions of Acute Angles Example: An acute angle is in standard position and its terminal side passes through ( 2 , 4 ). Find the values of the six trigonometric functions. sin θ = csc θ = cos θ = sec θ = tan θ = cot θ = 2 Algebra 2 Tuesday, April 07, 2009 Section 12.2: Trigonometric Functions of Acute Angles Pythagorean Identity: sin2 θ + cos2 θ = 1 Numerical Proof: Type this into your calc... sin230° + cos230° = ??? sin2320° + cos2320° = ??? Cofunction Identities: (think of complementary angles) sin ( 90° - θ ) = cos θ csc ( 90° - θ ) = sec θ cos ( 90° - θ ) = sin θ sec ( 90° - θ ) = csc θ tan ( 90° - θ ) = cot θ cot ( 90° - θ ) = tan θ Numerical Proof: Type this into your calc... sin (30°) = cos (90° - 30°) = 3 Algebra 2 Tuesday, April 07, 2009 Section 12.2: Trigonometric Functions of Acute Angles Example: Find the measure of acute angle θ, if cot θ = tan 20° 4