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ME3150 Trigonometric Identities

ME3150 Trigonometric Identities - Trigonometric Identities...

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Trigonometric Identities b a r b s r a = = = ) tan( ) ( co ) sin( θ θ θ π θ π π θ π θ θ θ π θ π θ π θ θ θ θ θ θ θ θ θ φ φ θ φ φ θ φ θ φ θ φ θ θ φ φ θ φ φ θ φ θ θ φ φ θ θ θ θ θ θ θ = = = = = = + + + = ± = + + ± = ± ± = ± = = + ) ( tan 2 / ) ( tan 2 / ; ) cos( ) sin( ) tan( ) ( cos 0 2 / ) ( sin 2 / ) ( sin 2 1 1 ) ( cos 2 ) ( sin ) ( cos ) 2 cos( ) cos( ) sin( 2 ) 2 sin( ) cos( ) sin( ) sin( ) cos( ) cos( ) cos( ) sin( ) sin( ) cos( ) cos( ) sin( ) sin( ) cos( ) cos( ) sin( ) sin( ) cos( ) sin( ) cos( ) sin( ) ( cos 1 ) sin( ) ( sin 1 ) cos( 1 ) ( sin ) ( cos 1 2 1 1 1 2 2 2 2 2 2 2 2 m 1st Quadrant: 2 / 0 1 π θ 0 ) tan( & ) sin( 1 1 θ θ , 0 ) cos( 1 θ 2nd Quadrant: π θ π 2 2 / 0 ) tan( & ) cos( 2 2 θ θ , 0 ) sin( 2 θ 3rd Quadrant: 2 / 3 π θ π 0 ) cos( & ) sin( 3 3 θ θ , 0 ) tan( 3 θ 4th Quadrant: 0 2 / 4 θ π 0 ) tan( & ) sin( 4 4 θ θ , 0 ) cos( 4 θ a ( = r sin θ ) b ( = r cos θ ) r θ sin tan cos θ 1 θ 4 θ 2 θ 3
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) sin( ) sin( θ θ = ) cos( ) cos( θ θ = ) sin( ) cos( 2 θ θ π = ) cos( ) sin( 2 θ θ π = ) cos( ) sin( 2 θ θ π = + ) sin( ) cos( 2 θ θ π = + 0 ) 0 sin( = 0 ) sin( = π 1 ) sin( 2 = π 1 ) sin( 2 = π 1 ) 0 cos( = 1 ) cos( = π 0 ) cos( 2 = π 0 ) cos( 2 = π For small 1 << θ rad: θ θ ) sin( 1 2 1 ) cos( 2 θ θ Combining sines & cosines:
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