Find sin2x, cos2x, and tan2x if cosx= -1/sqrt5 and x terminates in quadrant 3

Question

Find sin2x, cos2x, and tan2x if cosx= -1/sqrt5 and x terminates in quadrant 3. Hello, I'm stuck on this one problem and haven't been able to figure it out how the past minuite. Can anyone help me?

Answer 1

sin 2x = 2 sin x cos x

cos x = -1 / sqrt (5)

draw a right triangle with hypotenuse sqrt (5) and base leg 1.

Find the other side using pythagoras : it will be 2.

That means sin x = +- 2/ sqrt (5). The sine is negative in quadrant 3, so it will be - 2 / sqrt (5)

Now you can find sin (2x)

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

You can find this as you know cos x and sin x

tan (2x) = sin (2x) / cos (2x). Use the results you have just found to find tan (2x).