Given angle x, where 0 <= x < 360 (degrees), cos(x) is equal to a unique value.
Determine the value of to the nearest degree. Justify your answer.
To determine the value of cos(x) where 0 <= x < 360 degrees, we need to find the angle whose cosine value matches the given value.
Here's how you can find the angle using a scientific calculator or a cosine table:
1. Start by entering the given value of cos(x) into your calculator or find it in the table.
2. Press the inverse cosine function on your calculator, usually denoted as cos^(-1) or arccos. This function will give you the angle that produces the given cosine value.
3. After pressing the inverse cosine function, input the value obtained in the previous step (given cosine value). Make sure your calculator is set to degrees mode.
4. Press the "equals" button, and the calculator will provide the angle that satisfies the given cosine value.
For example, let's say cos(x) = 0.5. To find the value of x to the nearest degree:
1. Enter 0.5 into your calculator or find it in the cosine table.
2. Press the inverse cosine function, usually denoted as cos^(-1) or arccos.
3. Input 0.5 obtained in the previous step.
4. Press the "equals" button.
The calculator will give you the value of x, which is approximately 60 degrees.
Therefore, for cos(x) = 0.5, the value of x to the nearest degree is 60 degrees.