91Ó°ÊÓ

To convert an angle from degrees to radians, we need to use a straightforward formula. The formula to convert degrees to radians is: \[ \theta \text{(radians)} = \theta \text{(degrees)} \times \frac{\pi \text{ radians}}{180^{\circ}} \]. This formula leverages the fact that 180 degrees is equivalent to \(\pi\) radians.
For example, if we need to convert \(-60^{\circ}\) to radians, we substitute \(-60^{\circ}\) into the formula: \[ -60^{\circ} \times \frac{\pi \text{ radians}}{180^{\circ}} \]. At this stage, we have set up the problem for simplification.
Knowing how to convert degrees to radians is fundamental in trigonometry, especially when working with circular motion and periodic functions.

After setting up the initial conversion formula, the next step is to simplify the fraction. Starting with \( -60 \times \frac{\pi}{180} \), we need to reduce the fraction to its simplest form.
To simplify \( \frac{-60}{180} \), we look for the greatest common divisor (GCD). In this case, 60 is the GCD of both 60 and 180. By dividing both the numerator and the denominator by 60, we get \( \frac{-60}{180} = \frac{-1}{3} \).
So, the fraction simplifies to \( \theta \text{(radians)} =-\frac{\pi}{3} \).
Simplifying fractions is essential because it makes subsequent calculations easier and more understandable. A simplified fraction is always easier to work with, especially when you move to more complex operations or additional approximations.

Finally, we need to convert the simplified fraction to a decimal value, rounding to two decimal places as required. First, substitute \(\pi\) with its approximate value of 3.14:
\[ -\frac{3.14}{3} \text{≈ } -1.0467 \].
The problem requests rounding to two decimal places. Therefore, we round \(-1.0467\) to \(-1.05\).
Rounding is a common practice to make decimal values more manageable. These approximations are essential when precision is required up to a certain significant figure, especially in applied mathematics and practical problem-solving scenarios. When you approximate, always ensure the result meets the problem's requirements, as incorrect rounding can lead to errors in subsequent calculations.