mac1147_lecture23_1_c

mac1147_lecture23_1_c - 268 b a c β α L23 Complementary...

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Unformatted text preview: 268 b a c β α L23 Complementary Angles; Cofunctions; Trigonometric Functions of Angles 4 π , 6 π , 3 π ; Trigonometric Functions of General Angles Two acute angles are called complementary if their sum is the right angle. Example: Find the complementary angles for: (a) 50 ° (b) 2 7 π (c) 6 π Note : In a right triangle, 90 α β + = ° , therefore, α and β are complementary. Also, sin cos b c β α = = cos sin a c β α = = tan cot b a β α = = csc sec c b β α = = sec csc c a β α = = cot tan a b β α = = The functions sine & cosine, tangent & cotangent, and secant & cosecant are called cofunctions of each other. 269 Complementary Angles Theorem Cofunctions of complementary angles are equal. Note : The angles θ and 90 θ ° − are complementary, therefore, the theorem’s statement can be written as Function ( ) θ = Cofunction (90 ) θ ° − Or Function ( ) θ = Cofunction ( ) 2 π θ − Example : Use the Complementary Angle Theorem to fill in the blank spaces: sin10 cos ° = _____ cos30 sin ° = _____ tan cot 4 π = _____ csc sec 6 π = _____ Example : Find the exact values of the expressions. tan56 cot34 ° = ° 5 sin cos 12 12 π π − = 270 The Trigonometric Functions of Angles 4 π , 6 π , 3 π 45 4 π θ = = ° sin 4 π = csc 4 π = cos 4 π = sec 4 π = tan 4 π = cot 4 π = Example : Find the exact value of the expression....
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This note was uploaded on 11/07/2011 for the course MAC 1147 taught by Professor German during the Summer '08 term at University of Florida.

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mac1147_lecture23_1_c - 268 b a c β α L23 Complementary...

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