Question

The point P = (x, — 5/7) lies on the unit circle shown below. What is the value of xin simplest form?

Answer 1

The point (x,y) on unit circle is

`(x,y)=(\cos \theta,\sin \theta)`

We know y is "sin theta" and sin is "opposite" over "hypotenuse". Thus, we can draw a triangle

We see that "5" is opposite of theta and 7 is the hypotenuse.

To get x, we use the pythagorean theorem:

`\begin{gathered} \text{leg}^2+\text{AnotherLeg}^2=\text{Hypotenuse}^2 \\ x^2+5^2=7^2^{} \\ x^2+25=49 \\ x^2=49-25 \\ x^2=24 \\ x=\sqrt[]{24} \\ x=2\sqrt[]{6} \end{gathered}`

From unit circle formula, we know value of x is cos. Thus, we take the cosine ratio, adjacent over hypotenuse.

Adjacent is 2 Sqrt(6) and Hypotenuse is 7 Thus,

`x=\frac{2\sqrt[]{6}}{7}`