if cos x= 2/5, what is the measure of less than x, to the nearest degree?
To find the measure of angle x, based on the given cosine value, you can use the inverse cosine function, also known as arccos.
Let's calculate the inverse cosine of 2/5:
acos(2/5) ≈ 66.42°
Since cosine is positive in the first and fourth quadrants, the reference angle is also 66.42°. This means that there is another angle with the same cosine value in the fourth quadrant.
To find the measure of the angle less than x, we subtract the reference angle from 180°:
180° - 66.42° ≈ 113.58°
Therefore, to the nearest degree, the measure of the angle less than x is approximately 114°.
To find the measure of less than x, we need to determine the inverse cosine of 2/5.
Typically, we use inverse trigonometric functions such as arccosine (cos^−1) to find the angle whose cosine value matches a given ratio. However, to use the inverse cosine function, we need to ensure that the given ratio is within the valid range of -1 to 1.
Since the given ratio is 2/5, which falls within the valid range, we can proceed to find the inverse cosine of 2/5.
To find the inverse cosine value, we can use a scientific calculator or an online trigonometry tool.
Here's how you can find the measure of less than x using a scientific calculator:
1. Press the inverse cosine button (often denoted as cos^−1 or arccos) on your calculator.
2. Enter 2/5 as the input for the inverse cosine function.
3. Press the equals (=) button to get the inverse cosine value.
For example, let's use a scientific calculator to find the inverse cosine of 2/5:
- Press cos^−1 (or arccos).
- Enter 2/5.
- Press the equals (=) button.
The resulting value will give you the measure of less than x in radians. To convert radians to degrees, you can multiply the value by (180/π). Finally, round the result to the nearest degree.
Remember, the measure of less than x represents different angles depending on the quadrant in which x lies. Therefore, please specify the expected range or quadrant to get a precise answer.