Convert each angle measure to decimal degrees. If applicable, round to the nearest thousandth of a degree. See Example 4(a). 112° 15'

Verified step by step guidance

1. Understand that the angle is given in degrees and minutes, where 1 degree = 60 minutes.
2. Convert the minutes to a decimal by dividing the number of minutes by 60. In this case, convert 15' to decimal degrees by calculating \( \frac{15}{60} \).
3. Add the decimal result from the previous step to the whole number of degrees. This will give you the angle in decimal degrees.
4. Combine the whole number of degrees (112°) with the decimal obtained from the minutes conversion.
5. Round the final decimal degree value to the nearest thousandth if necessary.

Key Concepts

Degrees and Minutes

In trigonometry, angles can be measured in degrees, where one full rotation is 360 degrees. Each degree can be further divided into minutes, with one degree equal to 60 minutes. This notation is commonly used in navigation and astronomy, allowing for precise angle measurements.

Conversion to Decimal Degrees

To convert an angle from degrees and minutes to decimal degrees, you divide the minutes by 60 and add this value to the degrees. For example, to convert 112° 15', you calculate 15/60 = 0.25, resulting in 112.25 degrees. This conversion is essential for calculations in trigonometry that require angles in decimal form.

Rounding Numbers

Rounding is the process of adjusting a number to a specified degree of accuracy. In this context, rounding to the nearest thousandth means keeping three decimal places. For instance, if the result of a conversion is 112.250, it remains the same, but if it were 112.254, it would round to 112.254.