How do i do these trig functions?

Question

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

csc x = 9, tan x < 0

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

sec x = 4, x in Quadrant IV

Answer 1

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First get sin x which is 1/9. Then by soh cah toa you know opposite is 1 and hypotenuse is 9. That makes adjacent be √80 by Pythagorean, and since you'd have to be in quadrant 2 (sin is positive but tan is negative) you know cos x = -√80 / 9

sin 2x = 2 sin x cos x so just plug those in

cos 2x = cos^2 x - sin^2 x so plug in again'

then tan 2x = sin 2x / cos 2x

Do the other like that.