91Ó°ÊÓ

To solve problems involving trigonometric functions like tangent, it's often necessary to convert angles from degrees and minutes to decimal degrees.
Degrees can be broken down into smaller units called minutes, where one degree equals 60 minutes.
This conversion simplifies calculations and makes it easier to use with most calculators.

Here’s the simple formula to convert an angle from degrees and minutes to decimal degrees: To convert an angle: use the formula: \[ \text{Decimal Degrees} = \text{Degrees} + \frac{\text{Minutes}}{60} \]
For example, for 63 degrees and 48 minutes:
1. Divide the minutes (48) by 60, giving you 0.8.
2. Add this value to the degrees (63), resulting in 63.8 degrees.
Now, you have the angle in decimal degrees, which will make further calculations more straightforward.

Once we've converted the angle to decimal degrees, we can move forward with calculations.
Many trigonometric functions require this conversion, as calculators often do not accept inputs in the form of degrees and minutes.

Decimal degrees simplify the process by allowing us to work directly with a single numerical value.
For example, instead of working with 63 degrees and 48 minutes, we work with 63.8 degrees.
This is particularly useful when entering values into a calculator for trigonometric calculations, such as finding the tangent.

After calculating a trigonometric value like the tangent, it's essential to round your result to the desired number of decimal places.
This ensures consistency and precision in your answer.

Here are some steps to ensure accurate rounding:

• Identify the digit at the place to which you want to round. In our case, this is the fourth decimal place.
• Look at the digit immediately to the right. If it is 5 or higher, round up. If it is 4 or lower, leave the digit as is.
• Adjust the final digit accordingly and remove any remaining digits beyond it.

Using the example in our exercise, the result of \( \tan(63.8^{\text{°}}) \) is approximately 2.058914612.
Rounding this value to four decimal places results in 2.0589.
This rounded value is simpler to use and maintains the necessary precision.