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Math question help?

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 cos(x)=-9/11 with a domain of pi<x<3pi/2. Solve for following:

Cos(2x)
Sin(2x)
and Cos (1/2x)

I get how to do these types of questions if they are on the unit circle... but I am so stuck now with these...

Thanks!!!
Update : Oh yeah, and they dont want it in decimals too.    
asked Sep 18, 2014 in TRIGONOMETRY by anonymous

3 Answers

0 votes

(1)

cos(x)= -9/11

cos (2x) = 2cos²x - 1

             = 2(-9/11)² -1

             = 2( 81/121) -1

              = (162/121) - 1

              =(162 - 121)/121

              = 41/121

cos (2x) = 41/121

answered Sep 18, 2014 by friend Mentor
edited Sep 18, 2014 by bradely
0 votes

(3)

cos(x)= -9/11

image

answered Sep 18, 2014 by friend Mentor
0 votes

(2)

cos(x)= -9/11

sin (2x) = 2 sinx cosx

sinx = √(1 - cos² x)

sinx = √(1 - (81/121))

sinx = √(40/121)

sinx = √40 / 11

sinx = -√40 / 11       ( Since x is in 3rd quadrant sin x leads to negitive )

image

 

 
answered Sep 18, 2014 by friend Mentor

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