Question

In Exercises 99 through 1212, show the indicated angles graphically.

a. 240240^{\circ} \quad b. 405405^{\circ}

Solution

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(a)

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

mBOC=240°m\angle BOC=240\degree when point CC on the circle has coordinates (12,32)\left(\frac{-1}{2},\frac{-\sqrt{3}}{2}\right) since (cos240°,sin240°)=(12,32)(\cos 240\degree, \sin 240 \degree)=\left(\frac{-1}{2},\frac{-\sqrt{3}}{2}\right).

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