Homework Ch 53 Score 0 of 1 pt X 5351 Use the cosine of a su

Homework: Ch. 5.3 Score: 0 of 1 pt X) 5.3.51 Use the cosine of a sum and cosine of a difference identities to find cos (s+ t) and cos (s-t) 12 13 cos (s+t)- (Simplity your answer, including any radicals. Use integers or fractions for any numbers in the e

Solution

sin s = - 12/ 13

cos s =- sqrt ( 13^2 - 12^2 ) / 13 = - 5/ 13

sin t = 3/5

cos t = sqrt ( 5^2 - 3^2) / 5 = 4 / 5

applying cos (s+t) formula

cos (s+t) = cos Scos t - sin s sin t

= -5/13 * 4/5 + 12/ 13 * 3/5

= -20 / 65 + 36/65

= 16/65

cos (s - t) = cos s cos t + sin s sin t

= -5/13 * 4/5 - 12/ 13 * 3/5

= -20/65 - 36/65

= -56/65