Question

question convert the following angle from degrees to radians. express your answer in simplest form. 405°

Explanation:

Step1: Recall the conversion formula

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

Step2: Substitute the given angle

We have the angle \( 405^\circ \), so substitute into the formula: \( 405 \times \frac{\pi}{180} \)

Step3: Simplify the fraction

Simplify \( \frac{405}{180} \). Both numerator and denominator are divisible by 45. \( 405 \div 45 = 9 \) and \( 180 \div 45 = 4 \)? Wait, no, 405 ÷ 45 is 9? Wait, 45×9=405? 45×8=360, 45×9=405, yes. 180÷45=4? No, 45×4=180, yes. Wait, but 405 and 180 can also be divided by 15: 405÷15=27, 180÷15=12. Then 27 and 12 can be divided by 3: 27÷3=9, 12÷3=4. So \( \frac{405}{180}=\frac{9}{4} \)? Wait, no, 405÷180: divide numerator and denominator by 45: 405÷45=9, 180÷45=4? Wait, 45×9=405, 45×4=180, yes. So \( 405 \times \frac{\pi}{180}=\frac{405\pi}{180}=\frac{9\pi}{4} \) (after dividing numerator and denominator by 45: 405÷45=9, 180÷45=4)

Answer:

\( \frac{9\pi}{4} \)