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Trigonometry

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TRIG Identities Chapter 5

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Copyright ? 2009 Pearson Addison-Wesley 5.1-* 5 Trigonometric Identities Copyright ? 2009 Pearson Addison-Wesley Copyright ? 2009 Pearson Addison-Wesley 5.1-* 5.1 Fundamental Identities 5.2 Verifying Trigonometric Identities 5.3 Sum and Difference Identities for Cosine 5.4 Sum and Difference Identities for Sine and Tangent 5.5 Double-Angle Identities 5.6 Half-Angle Identities 5 Trigonometric Identities Copyright ? 2009 Pearson Addison-Wesley Copyright ? 2009 Pearson Addison-Wesley 1.1-* 5.1-* Fundamental Identities 5.1 Fundamental Identities ? Using the Fundamental Identities Copyright ? 2009 Pearson Addison-Wesley 1.1-* Copyright ? 2009 Pearson Addison-Wesley 1.1-* 5.1-* Fundamental Identities Reciprocal Identities Quotient Identities

Easy way to remember the positives and negatives of the trigonometric functions on a graph

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All you have to remember is " All Students Take Calculus" Stating from the first quad, its A for I, S for II, T for III, and C for IV. the acronyms stand for which of the functions are positive. A stands for all, all the functions are positive S stands for Sin, Only sin and csc are positive, rest are negative T stands for Tan, Only tan and cot are positive, rest are negative C stands for Cos, Only cos and sec are positive, rest are negative

Derivations of Trigonometry Formulas

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Given: sin(a+ b) = sin a cos b+ cos a sin b, we can figure out the following: sin(a? b) = sin(a+ (?b)) = sin a cos(?b) + cos a sin(?b) = sin a cos b+ cos a(? sin b) = sin a cos b? cos a sin b cos(a+b) = sin (pi 2 ? (a+ b) ) = sin ((pi 2 ? a ) ? b ) = sin (pi 2 ? a ) cos b?cos (pi 2 ? a ) sin b = cos a cos b?sin a sin b cos(a? b) = cos(a+ (?b)) = cos a cos(?b)? sin a sin(?b) = cos a cos b? sin a(? sin b) = cos a cos b+ sin a sin b tan(a+ b) = sin(a+ b) cos(a+ b) = sin a cos b+ cos a sin b cos a cos b? sin a sin b ? sec a sec b sec a sec b = sin a sec a+ sin b sec b 1? sin a sec a sin b sec b = tan a+ tan b 1? tan a tan b tan(a? b) = tan(a+ (?b)) = tan a+ tan(?b) 1? tan a tan(?b) = tan a+ (? tan b) 1? (? tan a tan b) = tan a? tan b 1 + tan a tan b

How to add fractions easilly

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My Pre-Cal teacher taught us this. When you are trying to add fractions during a sine or cosine problem, or something that has to do with a unit circle or a triangle, use this: Ex: 1/4 + 3/5 Multiply 5*1, multiply 4*3 and add them for the numberator, and multiply 4*5 for the denominator. So it would be 5+12/20. 17/20. You multiply the denominator of one and numerator of other by the denominator of other and numerator of one.Then add. That will give you the numerator. Then the denomnator you multiply both denominators and add.

Pre-Cal Trig Lesson

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1 Nov?23?6:28?AM Precalc?11.23.2010 We?are?going?to?learn?about?right?triangle?trigonometry. Nov?23?6:29?AM sohcahtoa?rules?on?a?right?triangle?and?the?new?trig? functions/ratios sine cosine tangent cotangent secant cosecant 2 Nov?23?6:31?AM 30?60?90?special?triangle?and?why? Nov?23?6:31?AM 45?45?90?special?triangle?and?why? 3 Nov?23?6:32?AM complementary?angle?relationships Nov?23?6:32?AM reciprocal?identities: 4 Nov?23?6:39?AM quotient?identities: Nov?23?6:40?AM pythagorean?identities: 5 Nov?23?6:42?AM know?the?mode?button?on?your?calculator! Nov?23?6:42?AM angle?of?elevation angle?of?depression 6 Nov?23?6:43?AM read?p.?280?286 p.?287?probs:??1?21(odds),?24,?27,?28,?32,?35,?37,?40,?41,? 45,?46,?47,?49,?51,?53,?59,?60,?61,?62,?64,?81

Trig Identities

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Pine Crest School Pre-Calculus Honors Handy Dandy Trigonometric Identities Reference Sheet RECIPROCAL IDENTITIES QUOTIENT IDENTITIES PYTHAGOREAN IDENTITIES sin2 x + cos2 x = 1 1 + cot2 x = csc2 x tan2 x + 1 = sec2 x SYMMETRY IDENTITIES cos (?x) = cos x sin (?x) = ? sin x tan (?x) = ? tan x CO-FUNCTION IDENTITIES = sin x = csc x = tan x ANGLE SUM IDENTITIES sin(x + y) = sin x cos y + cos x sin y sin(x ? y) = sin x cos y ? cos x sin y cos(x+y) = cos x cos y ? sin x sin y cos(x ? y) = cos x cos y + sin x sin y DOUBLE ANGLE IDENTITIES sin 2x = 2 sin x cos x cos 2x = cos2x ? sin2x = 2 cos2x ? 1 = 1 ? 2 sin2x HALF ANGLE IDENTITIES

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