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

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

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

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

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

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EXAMPLE 1 Solve a triangle for the SAS case Solve ABC with a = 11, c = 14, and B = 34°. SOLUTION Use the law of cosines to find side length b. b 2 = a.

EXAMPLE 1 Solve a triangle for the SAS case Solve ABC with a = 11, c = 14, and B = 34°. SOLUTION Use the law of cosines to find side length b. b 2 = a.

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