Question
In a rectangular coordinate system, a circle with center at the origin passes through the point $(2,2 \sqrt{3})$. What is the length of the arc on the circle in quadrant I between the positive horizontal axis and the point $(2,2 \sqrt{3})$ ?
Step 1
We can use the formula $\tan(\theta) = \frac{y}{x}$, where $(x,y)$ is the point $(2,2\sqrt{3})$. So, we have $\tan(\theta) = \frac{2\sqrt{3}}{2} = \sqrt{3}$. This gives us $\theta = \frac{\pi}{3}$. Show more…
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