Let u be an angle in the second quadrant with sinu = 2 /3 . Then cosu = ......and sin(2u) =........ .

Answer 1

sinu = 2/3

cosu <0 in quadrant II

cosu = -sqr(9-4)/3 = -(sqr5)/3

sin2u= 2sinucosu

= 2(2/3)(-sqr5/)3)

= (-4sqr5)/9

cosu is negative in quadrant II

construct a right triangle with height = 2, hypotenuse =3,

base =square root of (hypotenuse squared minus height squared)

= sqr(3^2-2^2) = sqr(9-4) = sqr5