Question

Find sin 2x, cos 2x and tan 2x under the given conditions:
cos x = -1/3, for π/2 < x < π

Answer 1

I know that first I need to find out what quadrant x is in, but I don't know how to do that.

Answer 2

you need two things. first is 'double angle' formulas, second is you are going to need to find
\[sin(x)\] in order to use them

Answer 3

sin2x=2sinx*cosx
cos2x=cos^2x-sin^2x

Answer 4

\[sin(x)=\frac{\sqrt{8}}{3}\] by pythagoras

Answer 5

K. Yeah my only problem is the first step, finding sin(x)

Answer 6

right . then use the formulas angela just sent you , replacing
\[cos(x)\] by -1/3 and \[sin(x)\] by \[\frac{\sqrt{8}}{3}\]

Answer 7

oh draw a right triangle. cosine is 1/3 so make the adjacent side 1 and the hypotenuse 3. use pythagoras to get the other side is
\[\sqrt{3^2-1^2}=\sqrt{8}\] so sin(x) = \[\frac{\sqrt{8}}{3}\]

Answer 8

oh okay thanks

Answer 9

or you can go straight to
\[sin(x)=\pm\sqrt{1-cos^2(x)}\] but then you have to deal with the annoying fractions under the radical