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7. Applications of Trigonometry

C. a. b. A. B. c. 7. Applications of Trigonometry. Sine Formula. Cosine Formula. a 2 = b 2 + c 2 - 2 bc cos A. b 2 = a 2 + c 2 - 2 ac cos B. c 2 = a 2 + b 2 - 2 ab cos C. 7. Applications of Trigonometry. (a) How to memorize the sine formula and the cosine formula?.

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7. Applications of Trigonometry

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  1. C a b A B c 7. Applications of Trigonometry Sine Formula Cosine Formula a2= b2 + c2 -2bc cos A b2= a2 + c2-2ac cos B c2= a2 + b2 -2ab cos C

  2. 7. Applications of Trigonometry (a) How to memorize the sine formula and the cosine formula? C C Sine Formula a b b a c b Oppositeside a B C A Opposite side Opposite side A B B A c c Where a, b and c represent the opposite sides of the angles A, B and C respectively. Sine FormulaEasy Memory Tips: In the formula, the alphabets of the numerator and the denominator A and a, Band b, C and c. are the same, like

  3. C a b ()2+()2-()2 A B c 2()() Remember the position of each symbol 7. Applications of Trigonometry (a) How to memorize the sine formula and the cosine formula? C Cosine FormulaEasy Memory Tips: a a b b cos( )= c Suppose the required angle is C. Cosine Formula 1. Put Con the L.H.S. c2= a2 + b2 -2ab cos C 2. Put the opposite side c of the angle C in the bracket after the minus sign 3. Put the remaining sides in the remaining brackets

  4. C A B c2= a2 + b2 -2ab cos C Using to find the length of AB. 7. Applications of Trigonometry (b) When to use the sine formula or the cosine formula? (Except the two cases below, the sine formula is preferred) Case I: two sides and the included angle are given Easy Memory Tips: We can denote “two sides and the included angle are given” as SAS. S A S The two S represent the given two sides AC and BC, A represents the given angle C.

  5. C A B b c b a Using to find. a b b c 2 + 2-2 cos = 2 7. Applications of Trigonometry (b) When to use the sine formula or the cosine formula? (Except the two cases below, the sine formula is preferred) Case II: three sides are given Easy Memory Tips: We can denote “three sides are given” as SSS. S S S b a c C A C B A B

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