Use the information given about the angle u 0 is less than o

Use the information given about the angle u, 0 is less than or equal to u is less than or equal to 2pi, to find the exact value of the indicated trigonometric function.

tan(u)=8/15, pi<u<3u/2 Find sin(2u)

Solution

tan u = 8/15      pi<= u < 3pi /2

tan theta = perpendicular / base

perpendicular = 8

base = 15

hypotenuse = sqrt ( 8^2 + 15^2) by pythagorean identity

hypotenuse = 17

sin u = perpendicular / hypotenuse = - 8/17

cos u = base / hypotenuse = - 15/17

plugging the values in teh formula

sin (2u) = 2 sin u cos u = 2 ( -8/17) ( -15/17) = 240 / 289

sin (2u) = 240 / 289