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https/www.webassign.net/web/Student/Assignment-Responses/submit dep- 13689012 o Show My Work (optional . O 03 points 1 Preous Answers LarATRMRP6 6 5 056 Find the exact values of sin(u/2), cos(u/2), and tan(u/2) using the half-angle formulas. 25 24 sin(u/2)25 cos(u/2) = tan(u/2) Need Help? L meen.LIinnt..Tuter. Show My Work Use the sun-to-product tormulas to wnits the sum or dfference as a product

Solution

cos u = 7/25

according to cos formula

cos theta = base / hypotenuse

base = 7

hypotenuse = 25

perpendicular = sqrt ( 25^2 - 7^2 ) = 24

therefore, sin u = perpendicular / hypotenuse = 24 / 25

tan u = perpendicular / base = 24 / 7

applying half angle formula

sin ( u/2) = + - sqrt {( 1- cos u ) / 2 } = + - sqrt ( 1 - 7/25)/2 = + - sqrt ( 18 / 50 ) = + - .6

cos (u/2) = + - sqrt {( 1+ cos u ) / 2 } = + - sqrt { 32/50 } = + - .8

tan (u/2) = sin u / ( 1+ cos u ) = 24/25 / ( 1+ 7/25) = 24/25 / 32/25 = 24 / 32