how many radians is 288°? give the exact answer in simplest form. radians
how many radians is 288°? give the exact answer in simplest form. radians
Answer
Explanation:
Step1: Use the degree - radian conversion formula
To convert degrees to radians, we use the formula: ( \text{Radians}=\frac{\pi}{180}\times\text{Degrees} ). Given the degree measure is ( 288^{\circ} ), substituting into the formula gives ( \frac{\pi}{180}\times288 ).
Step2: Simplify the fraction
Simplify ( \frac{288\pi}{180} ). First, find the greatest common divisor (GCD) of 288 and 180. The prime factorization of ( 288 = 2^{5}\times3^{2} ) and ( 180=2^{2}\times3^{2}\times5 ). The GCD of 288 and 180 is ( 36 ). Divide both the numerator and the denominator by 36: ( \frac{288\div36}{180\div36}\pi=\frac{8}{5}\pi ).
Answer:
(\frac{8}{5}\pi)