Question

the value 3pi/2 is a solution for the equation 2sin^2x-sinx-1=0

Answer 1

We want to FOIL this.

So I like to put things in terms of x if I have to foil it so I dont get confused so:

2x^2-x-1

So here's how we'd factor this, it's a basic one, really.

(2x+1)(x-1)

So now we just replace the xs with sin x and we factored it

(2sinx+1)(sinx-1)

Answer 2

So now we set each equal to zero to find what x equals:

So now what you do now is look up on your unit circle where sin equals 1 and where sin equals -1/2 and and those are your answers!