Question

I have two problems I am stuck on, if you could show me how to solve the problems it would be much appreciated.

1) Find sin 2x, cos 2x, and tan 2x from the given information.
tan x = − 1/6, cos x > 0

sin 2x =
cos 2x =
tan 2x =


2) Find sin 2x, cos 2x, and tan 2x from the given information.
cot x = 2/3, x in Quadrant I

sin 2x =
cos 2x =
tan 2x =

Answer 1

tan is - in quadrants 2 and 4
cos is + in quadrants 1 and 4
so
we are in quadrant 4, x = 6, y = -1
hypotenuse = sqrt (37) cute

tan 2x = 2 tan x /(1-tan^2 x)
= 2 (-1/6) /(1 - 1/36)
=-(1/3) / (35/36)
= -12/35 well that was easy

now we better find out what quadrant 2x is in
x is about - 10 degrees which is 350 degrees counterclockwise from x axis
so 2 x is about 700 degrees
700 - 360 = 340 or - 20
so
we are still in quadrant 4 (but you knew that :)

now
tan 2x= -12/35
draw that in quad 4
hypotenuse = sqrt (144+1225)
you do it, I call it h
then sin 2x = -12/h
and cos 2x = 35/h

Answer 2

Tan (x-10 degrees)+1=3