Trigonometry

May 19th, 2015
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6.1: Trigonometric Ratios sinθ = cosecθ 6.2: Fundamental Trigonometric Identities 6.3: The Cosine Rule 6.5: Sum and Difference of Angles (Extension 1) 6.6: Ratios of Double Angles (Extension 1)

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Chapter 6 Trigonometry6.1: Trigonometric Ratios 1sin = ------ cosec1 coscos = ------cot = ------ sec sin1 sintan = ------tan = ------ cot cos6.2: Fundamental Trigonometric Identitiessin + cos = 1- Substitute sin / cos into unit circle equation- Dividing through by sinsin cos 1 ------- + ------- = ------- 1 + cot = cosecsin sin sin- Dividing through by cossin cos 1 ------- + ------- = ------- 1 + tan = seccos cos cos6.3: The Cosine Rule b + c - acos A = -------------- 2bca = b + c - (2bc.cos A)6.4: The Sine Rule6.5: Sum and Difference of Angles (Extension 1)~ sin (A + B) = sinA . cosB + cosA . sinB~ sin (A B) = sinA . cosB cosA . sinBe.g: find the exact value of sin75sin75 = sin (45 + 30)= (sin45 . cos30) + (sin30 . sin45) 1 x 3 1 x 1 1 + 3= -------- + -------- = -------- 2 x 2 2 x 2 22~ cos (A + B) = cosA . cosB - sinA . sinB~ cos (A B) = cosA . cosB + sinA . sinBe.g: find the exact value of cos105cos105 = cos (60 + 45)

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