Question

# In Exercises $9$ through $12$, show the indicated angles graphically.a. $240^{\circ}$ $\quad$ b. $405^{\circ}$

Solution

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(a)

Shown below is the unit circle with center $O(0,0)$. Point $B(1,0)$ lies on the intersection of the circle and the X-axis.

$m\angle BOC=240\degree$ when point $C$ on the circle has coordinates $\left(\frac{-1}{2},\frac{-\sqrt{3}}{2}\right)$ since $(\cos 240\degree, \sin 240 \degree)=\left(\frac{-1}{2},\frac{-\sqrt{3}}{2}\right)$.