7 Applications of Trigonometry C Sine Formula a

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

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

7. Applications of Trigonometry (a) How to memorize the sine formula and the cosine formula? C Cosine Formula Easy Memory Tips: ( )2+( )2 -( )2 cos( ) = 2( ) Suppose the required angle is C. 1. Put C on the L. H. S. 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 a b A c Cosine Formula 2 2 2 c = a + b - 2 ab cos C Remember the position of each symbol B

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

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