Find sin(2x), cos(2x), and tan(2x) from the given information.

sin(x) = 5/13, x in Quadrant I
sin(2x)?
cos(2x)?
tan(2x)?

I honeslty just need one good example of how to do these please show all work and finalize answer

In QI, you have

sinx = 5/13
cosx = 12/13
tanx = 5/12

sin2x = 2sinx cosx = 2(5/13)(12/13) = 120/169

similarly using the other double-angle formulas.

How did you know ot multiple it with cos

because I studied the double-angle formulas, as you need to do!

Ok I know that the equation for

cos(2x)=1-2sin^2(x) How would you plug that in? It will not work

To find sin(2x), cos(2x), and tan(2x), we'll use double-angle formulas. Here's how you can do it step by step:

1. Given sin(x) = 5/13 and x in Quadrant I, we can determine the remaining trigonometric functions using the Pythagorean identity:
cos(x) = sqrt(1 - sin^2(x))
= sqrt(1 - (5/13)^2)
= sqrt(1 - 25/169)
= sqrt(144/169)
= 12/13
tan(x) = sin(x)/cos(x)
= (5/13)/(12/13)
= 5/12

2. Now, using the double-angle formulas, we can find sin(2x), cos(2x), and tan(2x):
sin(2x) = 2*sin(x)*cos(x)
= 2*(5/13)*(12/13)
= 120/169

cos(2x) = cos^2(x) - sin^2(x)
= (12/13)^2 - (5/13)^2
= 144/169 - 25/169
= 119/169

tan(2x) = sin(2x)/cos(2x)
= (120/169)/(119/169)
= 120/119

Therefore, sin(2x) = 120/169, cos(2x) = 119/169, and tan(2x) = 120/119.