Certainly! Let's find the measure of the angle whose cosine is 0.6, step by step:
1. Identify the Function and Value:
- We need to find the angle [tex]\( \theta \)[/tex] such that [tex]\( \cos(\theta) = 0.6 \)[/tex].
2. Inverse Cosine Function:
- To find [tex]\( \theta \)[/tex], we use the inverse cosine function, also known as arccosine. The angle [tex]\( \theta \)[/tex] is given by [tex]\( \theta = \arccos(0.6) \)[/tex].
3. Calculate the Radians:
- Using a calculator, [tex]\( \arccos(0.6) \)[/tex] is approximately [tex]\( 0.9273 \)[/tex] radians.
4. Convert Radians to Degrees:
- Since most angle measurements are typically expressed in degrees, we convert radians to degrees using the conversion factor [tex]\( 1 \text{ radian} \approx 57.2958 \text{ degrees} \)[/tex].
- [tex]\( 0.9273 \text{ radians} \times 57.2958 \text{ degrees/radian} \approx 53.13 \text{ degrees} \)[/tex].
5. Round to the Nearest Degree:
- Finally, we round [tex]\( 53.13 \text{ degrees} \)[/tex] to the nearest whole number, which gives us [tex]\( 53 \text{ degrees} \)[/tex].
Therefore, the measure of the angle to the nearest degree is [tex]\( 53 \text{ degrees} \)[/tex].
