Sin(x)=5/13 and x is in quadrant 1: find sin 2x, cos 2x, and tan 2x.?

Question

I know this is trigonometric double angle formula, but beyond that I’m stumped.

Lavinia Carroll · Accepted Answer

Identities needed: 1) sin 2x = 2 sin x cos x2) cos 2x = 2cos^2 x -13) cos x = √1-sin^2 x4) tan x = sin x / cos xsince sin x = 5/13, using identity (3) gives:cos x = √(1-25/169) = 12/13Using identity (2), it can be found that: >>>cos 2x = 2*(12/13)^2 -1 using identity (1):>>>sin 2x = 2* 5/13 * 12/13 = 120/169using identity (4):>>>tan 2x = [120/169] / [2*(12/13)^2 -1]

Lavinia Carroll · Answer

If sin x = 5/13 then cos x= 12/13Now, just apply the formulae and substitute the values of Sin x and Cos x Sin 2x = 2*Sin x*Cos x= 120/169Cos 2x = Cos^2 x – Sin^2 x = 144/169 – 25/169 =119/169Tan 2x = Sin 2x/Cos 2x = 120/119.

Lavinia Carroll · Answer

cos x = 12/13sin 2x = 2 sin x cos x = 2 x 5/13 x 12/13 = 120/169cos 2x = 2 cos ² x – 1 = 119/169tan 2x = 120/119

Lavinia Carroll · Answer

You’ll also need cos(x), which you can get by using sin^2(x) + cos^2(x) = 1. Solve for cos(x). You’ll have a choice of a positive or negative answer. The info that it’s in quadrant 1 tells you whether the cosine should be positive or negative.Once you have those, plug them into the formulas for sin(2x) and cos(2x), which are in terms of sin(x) and cos(x).And then tan(2x) = sin(2x)/cos(2x).

Alize Kuhn

Sin(x)=5/13 and x is in quadrant 1: find sin 2x, cos 2x, and tan 2x.?

4 Answers

AI-Powered Insights

Want to answer this question?

Categories

Tags

Related Questions