91Ó°ÊÓ

The cosine function, often denoted as \(\text{cos}\), is one of the fundamental trigonometric functions. It relates the ratio of the adjacent side to the hypotenuse of a right-angled triangle. In the context of the unit circle, the cosine of an angle \( \theta \) is the x-coordinate of the point where the terminal side of the angle intersects the circle.
When dealing with angles in radians, the cosine function remains the same. It calculates the same ratio but interprets the angle in radians instead of degrees. For instance, to evaluate \( \text{cos}(-1.91) \), we are working with an angle in the radian measure.
The cosine function has a range of values from \-1\ to \1\. Regardless of the angle input, the cosine function will always output a value within this range.

Radian mode is crucial when you are given an angle in radians. Calculators generally have two angle measurement modes: degrees and radians.
Radians are a way of measuring angles based on the radius of the circle. One full revolution around a circle is \(2\pi\) radians, which is equivalent to 360 degrees.
To switch your calculator to radian mode, look for the mode settings. You might see options like 'DEG' (for degrees) and 'RAD' (for radians). Select 'RAD' to switch to radian mode.
This is important because if your calculator is not in the correct mode, the values it computes for trigonometric functions will be incorrect for the given input.

Using a calculator to compute trigonometric functions involves a few careful steps:

• First, ensure that the calculator is set to the correct mode (radians, in this case).
• Next, carefully input the angle value. For example, enter \(-1.91\).
• Then, press the \( \text{cos} \) key to compute the cosine of the input angle.
• Finally, read the result displayed. For \( \text{cos}(-1.91) \), your calculator should show approximately -0.3331.

Double-checking each step ensures that you get accurate results. Remember to reset important settings to avoid errors in future calculations. Following these steps will help you consistently use your calculator effectively for trigonometric evaluations.