Problem 33 - Precalculus Essentials

Question

Convert each angle in degrees to radians. Round to two decimal places. $$200^{\circ}$$

Step-by-Step Solution

Answer

The angle \(200^{\circ}\) is approximately \(3.49\) radians when rounded to two decimal places.

Step 1: Understanding the Conversion Factor

To convert degrees to radians, one important concept must be clear: there are \(2\pi\) radians in a circle which is equivalent to \(360^{\circ}\). So, the conversion factor from degrees to radians is given by \(\frac{2\pi}{360^{\circ}}\) or simplifying it we get \(\frac{\pi}{180^{\circ}}\).

Step 2: Applying the Conversion Factor

To convert the given angle of \(200^{\circ}\) to radians, you will multiply it by the conversion factor \(\frac{\pi}{180^{\circ}}\). This gives us: \(200^{\circ} \times \frac{\pi}{180^{\circ}}\).

Step 3: Calculate the Result

Calculating the expression from step 2 gives approximately \(3.49\) in radians.

Step 4: Rounding off to Two Decimal Places

Rounding \(3.49\) to two decimal places will not change the number, it remains \(3.49\)