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PreCalculus-lulu

# PreCalculus-lulu - Lecture Notes on Precalculus Dr...

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Lecture Notes on Precalculus Dr. Eleftherios Gkioulekas

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Copyright c 2010 Eleftherios Gkioulekas. All rights reserved. Permission is granted to make and distribute verbatim copies of this document provided the copyright notice and this permission notice are preserved on all copies.
1 Contents PRE1: Review of geometry 4 PRE2: Trigonometric functions 10 PRE3: Trigonometric identities 39 PRE4: Trigonometric equations and inequalities 54 PRE5: Application to Triangles 85 PRE6: Vectors 104 PRE7: Sequences and series 124 PRE8: Conic sections 142

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Trigonometric identities a ± b 2 a sin( a ± b ) = sin a cos b ± sin b cos a cos( a ± b ) = cos a cos b sin a sin b tan( a ± b ) = tan a ± tan b 1 tan a tan b cot( a ± b ) = cot a cot b 1 cot b ± cot a (!!) = sin(2 a ) = 2 sin a cos a cos(2 a ) = cos 2 a sin 2 a = 2 cos 2 a 1 = 1 2 sin 2 a tan(2 a ) = 2 tan a 1 tan 2 a cot(2 a ) = cot 2 a 1 2 cot a sin( a + b ) sin( a b ) = sin 2 a sin 2 b cos( a + b ) cos( a b ) = cos 2 a

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