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question 4
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convert the following angle from degrees to radians. express your answer in simplest
form.
195°
answer
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π

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, use the formula: radians = degrees $\times\frac{\pi}{180}$.
So for $195^{\circ}$, it is $195\times\frac{\pi}{180}$.

Step2: Simplify the fraction

First, find the greatest common divisor (GCD) of 195 and 180.
The factors of 195 are 1, 3, 5, 13, 15, 39, 65, 195.
The factors of 180 are 1, 2, 3, 4, 5, 6, 9, 10, 12, 15, 18, 20, 30, 36, 45, 60, 90, 180.
The GCD of 195 and 180 is 15.
Divide both the numerator and denominator by 15: $\frac{195\div15}{180\div15}\times\pi=\frac{13}{12}\pi$.

Answer:

$\frac{13\pi}{12}$