Question

convert the angle in degrees to radians. - 75° - 75° = □ radians (simplify your answer. type an exact answer, using π as needed. use integers or fractions for any numbers in the expression)

Explanation:

Step1: Use the conversion formula

To convert degrees to radians, use the formula \( \text{Radians}=\text{Degrees}\times\frac{\pi}{180}\).
For \(- 75^{\circ}\), the conversion is \(-75\times\frac{\pi}{180}\).

Step2: Simplify the fraction

Simplify \(\frac{-75}{180}\).
Find the greatest common divisor (GCD) of \(75\) and \(180\). The factors of \(75\) are \(1,3,5,15,25,75\) and 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 \(75\) and \(180\) is \(15\).
Divide numerator and denominator by \(15\): \(\frac{-75\div15}{180\div15}=\frac{-5}{12}\).

Answer:

\(-\frac{5\pi}{12}\) radians