Precalculus

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

My answer is sqrt-15/8

• Precalculus -

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 -

wait i don't understand how you did your math?

• Precalculus -

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

• Precalculus -

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 -

you can do these a number of ways...

• Precalculus -

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

• Precalculus -

Awesome thanks mathmate!

• Precalculus :) -

You're welcome!

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