Question

Please help! :(
Find the exact value of sin(2u), cos(2u), and tan(2u) given that cos(u)=-(2/sqrt5), (pi/2) 10 years ago

Answer 1

pi/2 < u < u . . . . . I assume you mean pi/2 < u < pi ???
If so, u is in Q2, cos u < 0, sin u > 0

sin u = √(1 - cos²u)
sin u = √(1 - 4/9)
sin u = √(5/9)
sin u = √5/3

--------------------

sin 2u = 2 sin u cos u
sin 2u = 2 (√5/3) (-2/3)
sin 2u = -4√5/9

cos 2u = cos²u - sin²u
cos 2u = 4/9 - 5/9
cos 2u = -1/9

tan 2u = sin 2u / cos 2u
tan 2u = (-4√5/9) / (-1/9)
tan 2u = 4√5

--------------------

Calculating tan 2u using double-angle formula:
tan u = sin u / cos u
tan u = (√5/3) / (-2/3)
tan u = -√5/2

tan 2u = 2 tan u / (1 - tan²u)
tan 2u = 2 (-√5/2) / (1 - 5/4)
tan 2u = -√5 / (-1/4)
tan 2u = 4√5

Answer 2

Goodness, thank you again! You`re a lifesaver for sure <3

Answer 3

yw