Exercise (1) - No.2 Solutions

$\displaystyle \displaystyle \begin{array}{{|l|}}\hline \displaystyle 1\ \text{radian} = \frac{{180{}^\circ }}{\pi } \\ \hline \end{array}$

$\displaystyle \displaystyle \begin{array}{{|l|}}\hline \displaystyle \theta\ \text{radians} =\theta\times \frac{{180{}^\circ }}{\pi } \\ \hline \end{array}$

$ \displaystyle \text{(a)}\ 2\pi \ \text{rad}=\text{2}\pi \times \frac{{180{}^\circ }}{\pi }=360{}^\circ $

$ \displaystyle \text{(b)}\ \frac{{11\pi }}{6}\ \text{rad}=\frac{{11\pi }}{6}\times \frac{{180{}^\circ }}{\pi }=330{}^\circ $

$ \displaystyle \text{(c)}\ \frac{{7\pi }}{4}\ \text{rad}=\frac{{7\pi }}{4}\times \frac{{180{}^\circ }}{\pi }=315{}^\circ $

$ \displaystyle \text{(d)}\ \frac{{5\pi }}{3}\ \text{rad}=\frac{{5\pi }}{3}\times \frac{{180{}^\circ }}{\pi }=330{}^\circ $

$ \displaystyle \text{(e) }\frac{{3\pi }}{2}\ \text{rad}=\frac{{3\pi }}{2}\times \frac{{180{}^\circ }}{\pi }=270{}^\circ $

$ \displaystyle \text{(f) }\frac{{4\pi }}{3}\ \text{rad}=\frac{{4\pi }}{3}\times \frac{{180{}^\circ }}{\pi }=240{}^\circ $

$ \displaystyle \text{(g) }\frac{{5\pi }}{4}\ \text{rad}=\frac{{5\pi }}{4}\times \frac{{180{}^\circ }}{\pi }=225{}^\circ $

$ \displaystyle \text{(h) }\frac{{7\pi }}{6}\ \text{rad}=\frac{{7\pi }}{6}\times \frac{{180{}^\circ }}{\pi }=210{}^\circ $

$ \displaystyle \text{(i) }\pi \ \text{rad}=\pi \times \frac{{180{}^\circ }}{\pi }=180{}^\circ $

$ \displaystyle \text{(j) }\frac{{5\pi }}{6}\ \text{rad}=\frac{{5\pi }}{6}\times \frac{{180{}^\circ }}{\pi }=150{}^\circ $

$ \displaystyle \text{(k) }\frac{{3\pi }}{4}\ \text{rad}=\frac{{3\pi }}{4}\times \frac{{180{}^\circ }}{\pi }=135{}^\circ $

$ \displaystyle \text{(l) }\frac{{2\pi }}{3}\ \text{rad}=\frac{{2\pi }}{3}\times \frac{{180{}^\circ }}{\pi }=120{}^\circ $

$ \displaystyle \text{(m) }\frac{\pi }{2}\ \text{rad}=\frac{\pi }{2}\times \frac{{180{}^\circ }}{\pi }=90{}^\circ $

$ \displaystyle \text{(n) }\frac{\pi }{3}\ \text{rad}=\frac{\pi }{3}\times \frac{{180{}^\circ }}{\pi }=60{}^\circ $

$ \displaystyle \text{(o) }\frac{\pi }{4}\ \text{rad}=\frac{\pi }{4}\times \frac{{180{}^\circ }}{\pi }=45{}^\circ $

$ \displaystyle \text{(p )}\frac{\pi }{6}\ \text{rad}=\frac{\pi }{6}\times \frac{{180{}^\circ }}{\pi }=30{}^\circ $
 

Exercise (1) - No.1 Solutions

$\displaystyle \displaystyle\ \begin{array}{{|l|}}\hline \displaystyle 1{}^\circ =\frac{\pi }{{180}}\ \text{radians} \\ \hline \end{array}$

$\displaystyle \displaystyle \ \begin{array}{{|l|}}\hline \displaystyle \theta{}^\circ =\theta\times \frac{\pi }{{180}}\ \text{radians} \\ \hline \end{array}$  

$ \displaystyle \text{(a)}\ 30{}^\circ =30\times \frac{\pi }{{180}}=\frac{\pi }{6}\ \text{rad}$

$ \displaystyle \text{(b)}\ 45{}^\circ =45\times \frac{\pi }{{180}}=\frac{\pi }{4}\ \text{rad}$

$ \displaystyle \text{(c)}\ 60{}^\circ =60\times \frac{\pi }{{180}}=\frac{\pi }{3}\ \text{rad}$

$ \displaystyle \text{(d)}\ 90{}^\circ =90\times \frac{\pi }{{180}}=\frac{\pi }{2}\ \text{rad}$

$ \displaystyle \text{(e)}\ 120{}^\circ =120\times \frac{\pi }{{180}}=\frac{{2\pi }}{3}\ \text{rad}$

$ \displaystyle \text{(f)}\ 135{}^\circ =135\times \frac{\pi }{{180}}=\frac{{3\pi }}{4}\ \text{rad}$

$ \displaystyle \text{(g)}\ 150{}^\circ =150\times \frac{\pi }{{180}}=\frac{{5\pi }}{6}\ \text{rad}$

$ \displaystyle \text{(h)}\ 180{}^\circ =180\times \frac{\pi }{{180}}=\pi \ \text{rad}$

$ \displaystyle \text{(i)}\ 210{}^\circ =210\times \frac{\pi }{{180}}=\frac{{7\pi }}{6}\ \text{rad}$

$ \displaystyle \text{(j)}\ 225{}^\circ =225\times \frac{\pi }{{180}}=\frac{{5\pi }}{4}\ \text{rad}$

$ \displaystyle \text{(k)}\ 240{}^\circ =240\times \frac{\pi }{{180}}=\frac{{4\pi }}{3}\ \text{rad}$

$ \displaystyle \text{(l)}\ 270{}^\circ =270\times \frac{\pi }{{180}}=\frac{{3\pi }}{2}\ \text{rad}$

$ \displaystyle \text{(m)}\ 300{}^\circ =300\times \frac{\pi }{{180}}=\frac{{5\pi }}{3}\ \text{rad}$

$ \displaystyle \text{(n)}\ 315{}^\circ =315\times \frac{\pi }{{180}}=\frac{{7\pi }}{4}\ \text{rad}$

$ \displaystyle \text{(o)}\ 330{}^\circ =330\times \frac{\pi }{{180}}=\frac{{11\pi }}{6}\ \text{rad}$

$ \displaystyle \text{(p)}\ 360{}^\circ =360\times \frac{\pi }{{180}}=2\pi \ \text{rad}$