## Angles and Unit circle – exercises – pg.6/7

Posted in Math Problems by Lia on 05/01/2017

### 3. Find out the value of α in numerical radians (π ≅ 3.14):

${\color{Blue}&space;\textbf{a)}}\;&space;\;&space;\alpha=\frac{\textbf{2}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;&space;\alpha&space;=\frac{2\pi&space;}{3}$

### 4. Find what type of angle is “α“:

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha&space;=\textbf{235}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha&space;=\frac{\textbf{4}\pi}{\textbf{5}}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\alpha&space;=\textbf{77}^{\circ}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\alpha&space;=\frac{\textbf{5}\pi}{\textbf{4}}$

${\color{Blue}&space;\textbf{e)}}\;&space;\;\alpha&space;=\textbf{305}^{\circ}$

${\color{Blue}&space;\textbf{f)}}\;&space;\;\alpha&space;=\frac{\textbf{2}\pi}{\textbf{7}}$

${\color{Blue}&space;\textbf{g)}}\;&space;\;\alpha&space;=\textbf{154}^{\circ}$

### 5.  Find the complementary angle, β, of:

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha=\textbf{42}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha=\frac{\textbf{2}\pi&space;}{\textbf{5}}$

### 6.  Find the supplementary angle, β, of:

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha=\textbf{37}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha=\textbf{124}^{\circ}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\alpha=\frac{\textbf{2}\pi&space;}{\textbf{7}}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\alpha=\frac{\textbf{4}\pi&space;}{\textbf{5}}$

### 7.  Find the conjugate angle, β, of:

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha=\textbf{57}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha=\textbf{235}^{\circ}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\alpha=\frac{\textbf{2}\pi&space;}{\textbf{7}}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\alpha=\frac{\textbf{5}\pi&space;}{\textbf{4}}$

### 8. In what quadrant is the terminal side of α, when in standard position ?

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha&space;=\textbf{163}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha=&space;\frac{\textbf{6}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\alpha&space;=\textbf{73}^{\circ}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\alpha=&space;\frac{\textbf{13}\pi&space;}{\textbf{7}}$

${\color{Blue}&space;\textbf{e)}}\;&space;\;\alpha&space;=\textbf{215}^{\circ}$

${\color{Blue}&space;\textbf{f)}}\;&space;\;\alpha=&space;\frac{\textbf{2}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{g)}}\;&space;\;\alpha&space;=\textbf{310}^{\circ}$

${\color{Blue}&space;\textbf{h)}}\;&space;\;\alpha=&space;\frac{\textbf{6}\pi&space;}{\textbf{7}}$

### 9. Find the reference angle, β, when:

${\color{Blue}&space;\textbf{a)}}\;&space;\;\alpha&space;=\textbf{162}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\alpha=&space;\frac{\textbf{6}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\alpha&space;=\textbf{73}^{\circ}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\alpha=&space;\frac{\textbf{12}\pi&space;}{\textbf{7}}$

${\color{Blue}&space;\textbf{e)}}\;&space;\;\alpha&space;=\textbf{230}^{\circ}$

${\color{Blue}&space;\textbf{f)}}\;&space;\;\alpha=&space;\frac{\textbf{2}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{g)}}\;&space;\;\alpha&space;=\textbf{310}^{\circ}$

${\color{Blue}&space;\textbf{h)}}\;&space;\;\alpha=&space;\frac{\textbf{4}\pi&space;}{\textbf{7}}$

### Where: β is the angle shown below, α is the smallest coterminal angle and n is an integer that represents the number of times the angle rotates around the angle’s vertex when β is in standard position.

${\color{Blue}&space;\textbf{a)}}\;&space;\;\beta&space;=\textbf{395}^{\circ}$

${\color{Blue}&space;\textbf{b)}}\;&space;\;\beta&space;=&space;\frac{\textbf{16}\pi&space;}{\textbf{5}}$

${\color{Blue}&space;\textbf{c)}}\;&space;\;\beta&space;=\textbf{625}^{\circ}$

${\color{Blue}&space;\textbf{d)}}\;&space;\;\beta&space;=&space;\frac{\textbf{30}\pi&space;}{\textbf{7}}$

${\color{Blue}&space;\textbf{e)}}\;&space;\;\beta&space;=\textbf{1230}^{\circ}$

${\color{Blue}&space;\textbf{f)}}\;&space;\;\beta&space;=&space;\frac{\textbf{23}\pi&space;}{\textbf{3}}$

${\color{Blue}&space;\textbf{g)}}\;&space;\;\beta&space;=\textbf{910}^{\circ}$

${\color{Blue}&space;\textbf{h)}}\;&space;\;\beta&space;=&space;\frac{\textbf{41}\pi&space;}{\textbf{7}}$

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