# Simply Trig Expression

Tags: expression, simply, trig
 P: 26 1. The problem statement, all variables and given/known data Simplify the expression: cos(2sin^-1 (5x)) 2. Relevant equations Fundamental identities: 1 = sin^2 ϑ + cos^2 ϑ : I think you use this one? 3. The attempt at a solution Let y=2sin^-1(5x) sin y = 10x so, you plug in? 1 = 10x^2 + cos^2 y not really sure if im on the right path or what to do next
 Sci Advisor P: 1,128 Do you know a "double angle formula" that expresses cos(2t) in terms of sin(t)?
 P: 26 cos 2t = 1 - 2sin²t let t = sin^-1 5x so sin t = 5x cos 2t = 1 - 2(5x²) cos t = ( 1 - 2(5x²) ) / (2) is this correct?
P: 1,128

## Simply Trig Expression

 Quote by davemoosehead cos 2t = 1 - 2sin²t let t = sin^-1 5x so sin t = 5x cos 2t = 1 - 2(5x²) cos t = ( 1 - 2(5x²) ) / (2) is this correct?
cos(2t)=1-2(5x2) is almost correct; if t=arcsin(5x), what is sin2t ? But your last line is not correct. (Can you see why?) However, you don't need the last line; you have simplified the expression, and you're done!
 P: 26 sin²t = 5x²?
 P: 26 is cos 2t = 1 - 2(5x²) in simplest form? is that the answer?
 Sci Advisor P: 1,128 sin t = 5x, so sin2t=(5x)2=25x2. But I'm sure you knew that ...
 P: 26 Oh duh, ok from the start: cos(2 arcsin 5x) Let t = arcsin 5x so, sin t = 5x Since cos 2t = 1 - 2sin²t cos 2t = 1 - 2(5x)² cos 2t = 1 - 2(25x²)
 Sci Advisor P: 1,128 That's it. You might want to simplify it further to 1-50x2, but that's a minor detail.

 Related Discussions Calculus & Beyond Homework 5 Forum Feedback & Announcements 4 Calculus 13 Engineering, Comp Sci, & Technology Homework 2 Social Sciences 11