How do I find tan (2x)?

Question

If $\sin x=\frac{4}{7}$, x in quadrant I, then find (without finding x):

sin(2x)

cos(2x)

tan(2x)

Answer 1

Draw the geometry diagram

sinx= 4/7

cosx=√(33)/7

tanx=4/√(33

sin 2x =2sinxcosx

         = 2 ( 4/7)(√(33)/7)

        = 8√(33)/49

cos 2x = 2cos^2(x) -1

         =2(√(33)/7)^2 -1

         = 2(33/49)-1

          =17/49

Tan2x=sin2x/cos2x=[8√(33)/49]/[17/49] = 8sqrt(33)/17