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Published byCassidy Peel Modified about 1 year ago

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Trigonometry (1) Sine Rule Cosine Rule

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a b c x c-x h [Height] h 2 = b 2 - x 2 [Height] h 2 = a 2 - (c-x) 2 h 2 = a 2 - c 2 +2cx - x 2 A B C cos A = Adj/Hyp = x/b x = b cos A b 2 - x 2 = a 2 - c 2 +2cx - x 2 +x 2 b 2 = a 2 - c 2 +2cx b 2 = a 2 - c 2 +2c x b cos A a 2 = b 2 + c 2 - 2bc cos A The cosine rule proof - won’t be examined

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a 2 = b 2 + c 2 - 2bc cos A The Cosine Rule A B C a b c angles sides By similar proofs:- b 2 = a 2 + c 2 - 2ac cos B c 2 = a 2 + b 2 - 2ab cos C … is used for working out angles and sides in non-right angled triangles It is ….

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a 2 = b 2 + c 2 - 2bc cos A The Cosine Rule - example A B C 8 6 a ? angles sides a 2 = x 6 x 8 cos 75 Finding a side a =8.67 cm [2 d.p.] 75 o a 2 = x a 2 =

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a 2 = b 2 + c 2 - 2bc cos A The Cosine Rule - example A B C angles sides = x 7.1 x 8.8 cos A 2 x 7.1 x 8.8 cos A = Finding an angle cos A = = x 7.1 x 8.8 A = 116 o [to nearest degree] ?

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Activity Turn to page 71 of your Core 2 book and answer … Turn to page 71 of your Core 2 book and answer … exercise Bexercise B 1a) 1a) 2a) 2a)

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a b c h A B C sin A = Opp/Hyp = h/b The sine rule proof - won’t be examined sin B = Opp/Hyp = h/a h = b sin A h = a sin B h = b sin A = a sin B sin A sin B a = b sin B sin C b = c If the perpendicular was here

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The Sine Rule A B C a b c angles sides … is used for working out angles and sides in non-right angled triangles It is …. a = b = c sin A sin B sin C

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The Sine Rule - example A B C 4 cm angles sides Finding a side a = b = c sin A sin B sin C 35 o 75 o a ? a = b sin A sin B a = 4 sin 35 sin 75 a = 4 x sin 35 = = 2.4 cm [1dp] sin 75

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The Sine Rule - example A B C 6.5 cm angles sides Finding an angle a = b = c sin A sin B sin C ? 85 o 4 cm a = b sin A sin B 4 = 6.5 sin A sin 85 4 x sin 85 = 6.5 x sin A sin A = 4 x sin 85 = A = 38 o or = 162 o

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Activity Turn to page 74 of your Core 2 book and answer … Turn to page 74 of your Core 2 book and answer … exercise Cexercise C 1a) 1a) 3a) 3a)

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