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Convert the following radian measures to degrees: i) (7pi/12)c ii) (-5pi/3)c iii) 5c
Mathematics
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Step-by-step solution
12 stepsTo convert angles from radians (denoted by 'c') to degrees, we use the conversion factor:
- i) Convert to degrees.
Multiply the radian measure by the conversion factor.
$$ \left(\frac{7\pi}{12}\right)^c = \left(\frac{7\pi}{12} \times \frac{180}{\pi}\right)^\circ $$Cancel out and simplify the numerical values.
$$ = \left(\frac{7 \times 180}{12}\right)^\circ $$ $$ = (7 \times 15)^\circ $$ $$ = \boxed{\text{}105^\circ\text{}} $$- ii) Convert to degrees.
Multiply the radian measure by the conversion factor.
$$ \left(-\frac{5\pi}{3}\right)^c = \left(-\frac{5\pi}{3} \times \frac{180}{\pi}\right)^\circ $$Cancel out and simplify the numerical values.
$$ = \left(-\frac{5 \times 180}{3}\right)^\circ $$ $$ = (-5 \times 60)^\circ $$ $$ = \boxed{\text{} -300^\circ\text{}} $$- iii) Convert to degrees.
Multiply the radian measure by the conversion factor.
$$ 5^c = \left(5 \times \frac{180}{\pi}\right)^\circ $$Simplify the expression.
$$ = \left(\frac{900}{\pi}\right)^\circ $$Calculate the approximate numerical value (using ).
$$ = \left(\frac{900}{3.14159}\right)^\circ \approx 286.48^\circ $$ $$ = \boxed{\text{} \left(\frac{900}{\pi}\right)^\circ \approx 286.48^\circ\text{}} $$- iv) Convert to degrees.
Multiply the radian measure by the conversion factor.
$$ \left(\frac{11\pi}{18}\right)^c = \left(\frac{11\pi}{18} \times \frac{180}{\pi}\right)^\circ $$Cancel out and simplify the numerical values.
$$ = \left(\frac{11 \times 180}{18}\right)^\circ $$ $$ = (11 \times 10)^\circ $$ $$ = \boxed{\text{}110^\circ\text{}} $$- v) Convert to degrees.
Multiply the radian measure by the conversion factor.
$$ \left(-\frac{1}{4}\right)^c = \left(-\frac{1}{4} \times \frac{180}{\pi}\right)^\circ $$Simplify the expression.
$$ = \left(-\frac{180}{4\pi}\right)^\circ $$ $$ = \left(-\frac{45}{\pi}\right)^\circ $$Calculate the approximate numerical value (using ).
$$ = \left(-\frac{45}{3.14159}\right)^\circ \approx -14.32^\circ $$ $$ = \boxed{\text{} \left(-\frac{45}{\pi}\right)^\circ \approx -14.32^\circ\text{}} $$
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