Question

activity 2.3.1 - radians
answer the following questions. make sure to show all steps on how you got your answer.

1. convert from degrees to radians. you can type pi for the symbol π.

160°

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 degree value

We are given \(160^\circ\). Substitute this into the formula: \(\text{Radians} = 160\times\frac{\pi}{180}\)

Step3: Simplify the fraction

Simplify \(\frac{160}{180}\) by dividing both the numerator and the denominator by their greatest common divisor, which is 20. So, \(\frac{160\div20}{180\div20}=\frac{8}{9}\). Thus, the radian measure is \(\frac{8\pi}{9}\)

Answer:

\(\frac{8\pi}{9}\)