Question

use the given info to find sin2X, cos2X, tan2X:
sinX=(1/3), 0 12 years ago

Answer 1

Long problem..I will start you off........

First of all, x is a first-quadrant angle since it is given that 0 < x < pi/2.

1) sin (2x) = 2 sin(x) cos(x) = 2 (1/3)(sqrt(8))
If sin x = 1/3, draw a triangle to find the missing side by Pythagorean Theorem, and you get sqrt(8). So cos x = 1/3

I used the special double-angle formula for sin(2x) - 2 sin x cos(x).

Answer 2

Okay thanks, so now do I plug cos x = 1/3 into the double angle formula?

Answer 3

I plugged everything in for you to compute the first question, of finding sin(2x)

Answer 4

So I just solve it, right?

Answer 5

Oh sorry, I didn't get the first line right, I got it now. Thanks! So for cos and tan, do I use the double angle formula too?

Answer 6

Or how did you know to use that formula is a better question

Answer 7

for cos(2x), there are 3 formulas, so use any...but use the first formula which states that

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

Answer 8

or use cos(2x) = 1 - 2 sin^2(x)
= 1 - 2(1/3)^2
= 1 - 2/9
= 7/9

Answer 9

Okay awesome. So for tan I could use tan(2x) = (2tanx) / (1 - tan^2 x) ?