3.5 double & half angle

3.5 double & half angle - Math 114 Section 3.5...

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Unformatted text preview: Math 114 Section 3.5 Double-angle & Half-angle Formulas Section 2 A. Double-angle Formulas sin ( 2 ) = 2 sin cos = 1 - 2 sin 2 = 2 cos 2 - 1 2 tan tan ( 2 ) = 1 - tan 2 Find the exact values of the following trigonometric functions. 3 1. Given cos = , 0 < < , find 5 2 a) sin ( 2 ) cos( 2 ) = cos 2 - sin 2 b) tan ( 2 ) 2. Given tan = 1 3 , < < , find cos( 2 ) . 2 2 3. Given csc = - 5 , cos < 0 , find tan ( 2 ) . Use double-angle formulas to establish the following identities. 1. cot - tan = cos( 2 ) cot + tan 2. csc( 2 ) = 1 sec csc 2 3. cos( 2 ) cot - 1 = 1 + sin ( 2 ) cot + 1 B. Half-angle Formulas sin cos 1 - cos = 2 2 2 1 + cos where the + or - sign is determined by the quadrant of the angle of = 2 2 1 - cos tan = 2 sin sin 1 + cos = Find the exact values of the following trigonometric functions. 1. cos 22.5 2. tan 7 12 3 3. sin - 8 4. Given sin = - 3 3 < < 2 , find cos . , 2 2 3 5. Given sec = 2, csc < 0 , find sin . 2 Use half-angle formulas to establish the following identities. 2 1. csc 2 = 2 1 - cos 2. tan = csc - cot 2 Find the exact value of each expression. 3 -1 1. sin 2 sin 2 -1 4 2. cos 2 cos 5 2 1 -1 3 3. cos sin 5 2 ...
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3.5 double &amp; half angle - Math 114 Section 3.5...

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