How do you prove this?

Question

Is sin2xsinx-cosx = -(3root3)/2 true for 7pi/6? Explain.

Answer 1

Let's break down the three components.

 

sin(2x)

=sin(2(7pi/6))

=sin(7pi/3)

=sin(pi/3)        (using the rule sin(a+2pi) = sin(a)

=√3/2                (Quadrant I, pi/3 family)

 

sin(x)

=sin(7pi/6)

=-1/2                (Quadrant III, pi/6 family)

 

cos(x)

=cos(7pi/6)

=-√3/2              (Quadrant III, pi/6 family)

 

Now we can put our elements together in the original equation.

sin(2x)sin(x)-cos(x)

=(√3/2)(-1/2)-(-√3/2)

=-√3/4+√3/2

=-√3/4+2√3/4

=V3/4

 

Thus the -(3root3)/2 answer is false.