Question

Suppose that (x,square root7/3) is a point in quadrant 1 lying on the unit circle. Find x

Answer 1

Answer: x ≈ 0.4714

Step-by-step explanation

Suppose that:

`(x,(√(7))/(3))`

Then, we can build the following:

Then, as we know that the coordinates of the unis circle is (x=cos θ, y=sin θ), and we have the value of y, then we can solve for θ and then get cos θ.

0. Isolating for θ:

`(√(7))/(3)=\sin(\theta)`
`\sin^(-1)((√(7))/(3))=\sin^(-1)(\sin(\theta))`
`\theta=\sin^(-1)((√(7))/(3))\approx61.87\degree`

2. Calculating cos (θ):

`x=\cos\theta=\cos(61.87)\approx0.4714`