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

Question

Given that sin(x) = 5/13 and x is in the first quadrant, how can I calculate sin(2x), cos(2x), and tan(2x) using the double-angle formulas? I understand this involves trigonometric identities, but I’m unsure how to proceed from here. Could someone guide me through the steps?

Anonymous · Accepted Answer

Identities needed:1) sin 2x = 2 sin x cos x2) cos 2x = 2cos^2 x -13) cos x = &radic;1-sin^2 x4) tan x = sin x / cos xsince sin x = 5/13, using identity (3) gives:cos x = &radic;(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]

Dr. Nathen Kerluke · Answer

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

Anonymous · Answer

cos x = 12/13

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

Madelyn Ebert DDS · 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).

Ms. Estel Rempel V

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

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