Answer: (i) This angle is 33.41% of the full rotation.
(ii) 120.38°
Step-by-step explanation:
GIven: Measure of full rotation = 2π radians
Measure of an angle = 2.1 radians.
The percent of this angles of a full rotation = [tex]\dfrac{2.1}{2\pi}\times100\%[/tex]
[tex]=\dfrac{2.1\times7}{2\times22}\times100\% \ \ \ \ [\pi =\dfrac{22}{7}]\\\\=33.41\%[/tex]
i.e. This angle is 33.41% of the full rotation.
In degrees,
[tex]\text{ 2.1 radians}=2.1\times\dfrac{180}{\pi}\\\\=2.1\times\dfrac{180}{3.14}\approx120.38^{\circ}[/tex]
[tex]2.1\text{ radians}[/tex] is [tex]33.4\%[/tex] of a full rotation and is equivalent to [tex]120.2^\circ[/tex]
The relationship between degree and radian measures is
[tex]1\text{ radian}=\dfrac{180}{\pi}^\circ[/tex]
We want to express [tex]2.1\text{ radians}[/tex] as a percentage of a full rotation.
[tex]\dfrac{2.1}{2\pi}\times100\%=\dfrac{210}{2\pi}\%\\\\\approx33.4\%[/tex]
How do we determine the measure of an angle (in degrees) given the percentage? Simply multiply the percentage by the complete/full rotation (that is [tex]360^\circ[/tex])
[tex]33.4\%\times360^\circ\\\\=\dfrac{33.4}{100}\times360^\circ\\\\\approx120.2^\circ[/tex]
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