OpenStudy (anonymous):

Please help! :(
Find the exact value of sin(2u), cos(2u), and tan(2u) given that cos(u)=-(2/sqrt5), (pi/2)__
1 year ago
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OpenStudy (janu16):

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

1 year ago
OpenStudy (anonymous):

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

1 year ago
OpenStudy (janu16):

yw

1 year ago