Precalculus
posted by Jess .
If sinx= 1/4 and x terminates in the third quadrant, find the exact value of sin2x
My answer is sqrt15/8

Precalculus 
bobpursley
sin2x=2sinx cos x
= 2*.25*cos x but
sin^2x+cos^2x=1 so
cos^2x=.75
cosx=sqrt 3/4
so now you have it.
check sign: if x is in the third quadrant, so 2x will be in the second quadrant, where sine is + 
Precalculus 
Jess
wait i don't understand how you did your math?

Precalculus 
Jess
dont you use the formula sin2 theta =2sintheta cos theta?

Precalculus 
Jess
I used that formula sin^2x+cos2x=1
1/4 squared minus that by one and squareroot it square root of 15 over 4 
Precalculus 
bobpursley
you can do these a number of ways...

Precalculus 
MathMate
I get
cos(x)
=sqrt(1sin^2(x))
=sqrt(1(1/4)^2)
=sqrt(15/16)
so
sin(2x)
=+2sin(x)cos(x)
=+2*(1/4)sqrt(15/16)
=sqrt(15) / 8 
Precalculus 
Jess
Awesome thanks mathmate!

Precalculus :) 
MathMate
You're welcome!
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