Asked by Jess

If sinx= -1/4 and x terminates in the third quadrant, find the exact value of sin2x


My answer is sqrt-15/8
Answered by 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 +
Answered by Jess
wait i don't understand how you did your math?
Answered by Jess
dont you use the formula sin2 theta =2sintheta cos theta?
Answered by 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
Answered by bobpursley
you can do these a number of ways...
Answered by MathMate
I get
cos(x)
=sqrt(1-sin^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
Answered by Jess
Awesome thanks mathmate!
Answered by MathMate
You're welcome!
Answered by Jazzzzz
Hello from the future
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