sinx = 5/13 , x is in Quadrant 1. Find Sin2x, cos2x, and tan2x

Question

sinx = 5/13 , x is in Quadrant 1. Find Sin2x, cos2x, and tan2x

Answer 1

I didn't finish these problems due to time constraints of 5 minutes so let me know if you need more help and I will post another video!

Answer 2

adjacent side = sqr(169-25) =sqr144 = 12

cosx= 12/13, sinx=5/13

sin2x= 2sinxcosx = 2(5/13)(12/13) = 120/169

cos2x = cos^2(x)-sin^2(x) = 144/169 - 25/169= 119/169

tan2x = sin2x/cos2x = 120/119

or sinx =5/13 x = sin^-1(5/13) = about 22.62 degrees

2x =45.24

sin45.24 = 0.710 virtually the same as 120/169

cos45.24= 0.704 same as 119/169 for 3 decimal places

tan45.24 = 1.008 same as 120/119