Express the following angles in radians: (a) 45.0°, (b) 60.0°, (c) 90.0°, (d) 360.0°, and (e) 445°. Give as numerical values and as fractions of \(\pi \).

To change the angle from degree to radian, you should multiply it by \(\frac{\pi }{{{{180}^ \circ }}}\).

Part (a)

Now, expressing \({45.0^ \circ }\) in radians unit, you get:

\(\begin{aligned}{45.0^ \circ } &= {45.0^ \circ } \times \frac{\pi }{{{{180}^ \circ }}}\;{\rm{rad}}\\ &= \frac{\pi }{4}\;{\rm{rad}}\end{aligned}\)

Part (b)

Express \({60^ \circ }\) in radians unit.

\(\begin{aligned}{60^ \circ } &= {60^ \circ } \times \frac{\pi }{{{{180}^ \circ }}}\;{\rm{rad}}\\ &= \frac{\pi }{3}\;{\rm{rad}}\end{aligned}\)

Part (c)

Now, expressing \({90^ \circ }\) in radians unit, you get:

\(\begin{aligned}{90^ \circ } &= {90^ \circ } \times \frac{\pi }{{{{180}^ \circ }}}\;{\rm{rad}}\\ &= \frac{\pi }{2}\;{\rm{rad}}\end{aligned}\)

Part (d)

Express \({360^ \circ }\) in radians unit.

\(\begin{aligned}{360^ \circ } &= {360^ \circ } \times \frac{\pi }{{{{180}^ \circ }}}\;{\rm{rad}}\\ &= 2\pi \;{\rm{rad}}\end{aligned}\)

Part (e)

Now, expressing \({360^ \circ }\) in radians unit, you get:

\(\begin{aligned}{445^ \circ } &= {445^ \circ } \times \frac{\pi }{{{{180}^ \circ }}}\;{\rm{rad}}\\ &= \frac{{89\pi }}{{36}}\;{\rm{rad}}\end{aligned}\)