convert the angle in degrees to radians. - 75° - 75° = □ radians (simplify your answer. type an exact…

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)

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)

Answer

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