Trig Identities

Trig Identities - TRIGONOMETRIC IDENTITIES The six...

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Tom Penick [email protected] www.teicontrols.com/notes 2/20/2000 TRIGONOMETRIC IDENTITIES The six trigonometric functions : sin θ = = opp hyp y r csc sin θ θ = = = hyp opp r y 1 cos θ = = adj x r sec cos θ θ = = = hyp adj r x 1 tan sin cos θ θ θ = = = opp adj y x cot tan θ θ = = = adj opp x y 1 Sum or difference of two angles : sin ( ) sin cos cos sin a b a b a b ± = ± cos( ) cos cos sin sin a b a b a b ± = m tan( ) tan tan tan tan a b a b a b ± = ± 1 m Double angle formulas : tan tan tan 2 2 1 2 θ θ θ = - sin sin cos 2 2 θ θ θ = cos cos 2 2 1 2 θ θ = - cos sin 2 1 2 2 θ θ = - cos cos sin 2 2 2 θ θ θ = - Pythagorean Identities : sin cos 2 2 1 θ θ + = tan sec 2 2 1 θ θ + = cot csc 2 2 1 θ θ + = Half angle formulas : sin ( cos ) 2 1 2 1 2 θ θ = - cos ( cos ) 2 1 2 1 2 θ θ = + sin cos θ θ 2 1 2 = ± - cos cos θ θ 2 1 2 = ± + tan cos cos sin cos cos sin θ θ θ θ θ θ θ 2 1 1 1 1 = ± - + = + = - Sum and product formulas : sin cos [sin( ) sin( )] a b a b a b = + + - 1 2 cos sin [sin ( ) sin ( )] a b a b a b = + - - 1 2 cos cos [cos( ) cos( )] a b a b a b = + + - 1 2 sin sin [cos ( ) cos ( )] a b a b a b = - - + 1 2 ( 29 ( 29 sin sin sin cos a b
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This note was uploaded on 04/24/2008 for the course CHEM 202 taught by Professor Motle during the Spring '08 term at Rose-Hulman.

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Trig Identities - TRIGONOMETRIC IDENTITIES The six...

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