The cosine function (cos) has a value of zero at specific angles. According to the provided reference, the value of cos is zero at two angles: 90 degrees and 270 degrees.
Cosine Values at Key Angles
The following table summarizes cosine values at key angles, based on the reference provided:
| Degree | cosθ |
|---|---|
| 60° | 1/2 |
| 90° | 0 |
| 180° | -1 |
| 270° | 0 |
Explanation
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Cosine and the Unit Circle: Cosine is defined as the x-coordinate of a point on the unit circle. When the angle is 90 degrees or 270 degrees, the x-coordinate is 0, hence cos(90°) = 0 and cos(270°) = 0.
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Periodicity of Cosine: The cosine function is periodic, meaning it repeats its values in intervals. Cosine has a period of 360 degrees. This means the cosine values will be zero again after multiples of 360 degrees have been added to the initial angles (90° and 270°)
Additional Insights
- While not mentioned in the reference, it is important to note that cos(x) = 0 at angles of 90° + n*180° where n is an integer. For example:
- when n=0 we get 90°
- when n=1 we get 270°
- when n=2 we get 450°
- when n=-1 we get -90°
- The reference clearly shows that at 90° and 270° cos is zero.
Therefore, the value of cos is zero at angles of 90 degrees and 270 degrees.
