Final answer:
To approximate cos⁻¹(0.25), enter 0.25 into the calculator and press the inverse cosine function key. The calculator will provide an angle measure, usually in degrees. The angle will be between 75 and 90 degrees and should be rounded to an appropriate number of significant figures.
Step-by-step explanation:
To approximate the value of cos⁻¹(0.25) using a calculator, you would typically enter 0.25 and then press the inverse cosine function, often labeled as 'cos⁻¹', 'cos', or sometimes 'cos⁻¹' within a shift or second function menu depending on the calculator model. Once you press the equal sign or 'ENTER', the calculator will display the angle in degrees or radians, according to the mode you're in (degree mode by default for many calculators).
The actual steps to perform this function can vary depending on whether you are using a scientific calculator, a graphing calculator such as the TI-83, 83+, or 84+ series, or even a calculator app on a smartphone or computer. The inverse cosine of 0.25 generally results in an angle larger than 75 degrees but smaller than 90 degrees, as the cosine decreases as the angle increases from 0 to 90 degrees.
The approximation provided by the calculator should be considered to be a few significant figures to maintain precision in your result.