10 Section 2.2 The Unit Circle

1.  Convert the following angles from degrees to radians, or radians to degrees, as appropriate.

a. [latex]\frac{20\pi}{3}[/latex] radians

b. [latex]-240^\circ[/latex]

c. [latex]190^\circ[/latex]

d. [latex]\frac{23\pi}{4}[/latex] radians

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Answers

a. [latex]1200^\circ[/latex]

b. [latex]-\frac{4\pi}{3}[/latex]

c. [latex]\frac{19\pi}{18}[/latex]

d. [latex]1035^\circ[/latex]

 

2.  For each of the given angles, find the exact coordinates on the unit circle.

a. [latex]-\frac{7\pi}{6}[/latex]

b. [latex]-\frac{7\pi}{4}[/latex]

c. [latex]\frac{23\pi}{4}[/latex]

d. [latex]17\pi[/latex]

e. [latex]-5\pi[/latex]

f. [latex]-\frac{11\pi}{6}[/latex]

g. [latex]\frac{31\pi}{6}[/latex]

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Answers

a. [latex](-\frac{\sqrt3}{2}, \frac{1}{2})[/latex]

b. [latex](\frac{\sqrt2}{2}, \frac{\sqrt2}{2})[/latex]

c. [latex](\frac{\sqrt2}{2}, -\frac{\sqrt2}{2})[/latex]

d. [latex](-1,0)[/latex]

e. [latex](-1,0)[/latex]

f. [latex](\frac{\sqrt3}{2}, \frac{1}{2})[/latex]

g. [latex](-\frac{\sqrt3}{2}, -\frac{1}{2})[/latex]

 

 

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