Question

write 270° in radians as a multiple of π. a) \\(\frac{4pi}{3}\\) b) \\(\frac{3pi}{2}\\) c) \\(\frac{5pi}{4}\\) d) \\(\frac{4pi}{2}\\)

Explanation:

Step1: Recall the conversion formula

To convert degrees to radians, we use the formula: \( \text{radians} = \text{degrees} \times \frac{\pi}{180^\circ} \).

Step2: Substitute the given degree measure

We have \( 270^\circ \), so substitute into the formula: \( 270^\circ \times \frac{\pi}{180^\circ} \).

Step3: Simplify the fraction

Simplify \( \frac{270}{180} \). Both numerator and denominator are divisible by 90: \( \frac{270\div90}{180\div90} = \frac{3}{2} \). So the result is \( \frac{3\pi}{2} \).

Answer:

B) \( \frac{3\pi}{2} \)