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

Explanation

Suppose that:

$(x,\frac{\sqrt{7}}{3})$

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:

$\frac{\sqrt{7}}{3}=\sin(\theta)$$\sin^{-1}(\frac{\sqrt{7}}{3})=\sin^{-1}(\sin(\theta))$$\theta=\sin^{-1}(\frac{\sqrt{7}}{3})\approx61.87\degree$

2. Calculating cos (θ):

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