Math  /  Trigonometry

QuestionHow many radians is 100100^{\circ} ? (Give the exact answer in simplest forr \begin{tabular}{|c|} \hline Answer \\ \hline radians \\ \hline \end{tabular}

Studdy Solution

STEP 1

1. The conversion factor between degrees and radians is π180 \frac{\pi}{180} .
2. We need to convert 100 100^\circ to radians.

STEP 2

1. Understand the conversion factor.
2. Apply the conversion factor to the given angle.
3. Simplify the expression to its simplest form.

STEP 3

The conversion factor from degrees to radians is π180 \frac{\pi}{180} . This means that to convert degrees to radians, we multiply the degree measure by π180 \frac{\pi}{180} .

STEP 4

To convert 100 100^\circ to radians, we multiply 100 100 by the conversion factor π180 \frac{\pi}{180} :
100×π180 100^\circ \times \frac{\pi}{180}

STEP 5

Perform the multiplication:
100π180 \frac{100 \pi}{180}

STEP 6

Simplify the fraction 100180 \frac{100}{180} by finding the greatest common divisor (GCD) of 100 100 and 180 180 , which is 20 20 .

STEP 7

Divide both the numerator and the denominator by their GCD:
100÷20180÷20=59 \frac{100 \div 20}{180 \div 20} = \frac{5}{9}
Thus, the expression simplifies to:
5π9 \frac{5\pi}{9}
The exact answer in simplest form is:
5π9 \boxed{\frac{5\pi}{9}}

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