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To find an angle when given its cosine value, we use the inverse cosine function, written as \(\text{cos}^{-1}\). This function allows us to determine the angle whose cosine is a specified value.
For example, if \(\text{cos B} = 0.6\), to find the angle \(\text{B}\), use \(\text{B} = \text{cos}^{-1}(0.6)\).
Note: The cosine function returns a value between -1 and 1, so the input for \(\text{cos}^{-1}\) must also be within this range.
Always remember to use a calculator or trigonometric tables to find this value. Calculators often have a button labeled \( \text{cos}^{-1}\) for this purpose.
In this example, \( \text{cos}^{-1}(0.6) \) approximately equals 53.13 degrees. This means the angle whose cosine is 0.6 is roughly 53.13 degrees.

Angles can be measured in degrees or radians, but for most trigonometric problems at this level, degrees are used. A full circle measures 360 degrees.
Make sure your calculator is set to 'Degree' mode before performing trigonometric calculations.
If your calculator is in 'Radian' mode, it will provide results in radians, which can be confusing if you're expecting degrees.
For instance, \( \text{cos}^{-1}(0.6) \) in 'Degree' mode is 53.13 degrees.
In a different context, you might encounter the same problem being solved in 'Radian' mode, which would yield approximately 0.927 radians. Hence, for clarity and accuracy in problem-solving, the mode of your calculator is crucial.

When instructed to round to the nearest degree, look at the decimal part of the angle.
If it is 0.5 or higher, round up. If it is less than 0.5, round down.
For example, our calculated angle from \( \text{cos}^{-1}(0.6) \) is 53.13 degrees.
Since the decimal 0.13 is less than 0.5, we round down, making the angle 53 degrees.
This rounding process ensures the angle measure is simple and easy to work with in practical situations.
Remember, this rule of rounding applies universally across mathematical and everyday contexts for ease and consistency.