Convert the following angle from degrees to radians. Express your answer in terms of  and in simplest form.60°60°

1. Break Down the Problem

To convert an angle from degrees to radians, we will use the conversion factor that $\pi \text{ radians} = 180^\circ$. Therefore, to convert degrees to radians, we multiply the degree measure by $\frac{\pi}{180}$.

2. Relevant Concepts

The formula for converting degrees to radians is: $\text{Radians} = \text{Degrees} \times \frac{\pi}{180}$

3. Analysis and Detail

Now we will apply the formula to convert $60^\circ$ to radians: $\text{Radians} = 60 \times \frac{\pi}{180}$ Simplifying this: $\text{Radians} = \frac{60\pi}{180}$ This can be further simplified by dividing both the numerator and the denominator by 60: $\text{Radians} = \frac{\pi}{3}$

4. Verify and Summarize

We verify that the calculation is correct by checking the simplification: $60\pi \div 60 = \pi \quad \text{and} \quad 180 \div 60 = 3$ Thus, $\frac{60\pi}{180}$ simplifies to $\frac{\pi}{3}$.

Final Answer

The angle $60^\circ$ in radians is $\frac{\pi}{3}$.