Question

The radian measure of an angle that is 105 degrees 32' 45'' is?

a. 1.59 radians
b. 1.84 radians
c. 0.59 radians
d. 2.78 radians

Answer 1

\[2\pi^r=360°\]\[\pi^r=180°\]
\[\frac{\pi^r}{180°}=1\]

\[\theta°=\theta°\times1=\theta°\times\frac{\pi^r}{180°}=\frac{\theta}{180}\times\pi^r\]

Answer 2

\[105°32'45''=105°+32'\times\frac{1°}{60'}+45''\times\frac{1°}{60'}\times\frac{1'}{60''}\]