When is cosα a x component or y component in a problem?

[pillar]

How when do you know when to use cosα in the x component or y component?

I thought you only use cosα on the x component since it's the x coordinate on the unit circle.

Can somebody give me an example, I would appreciate it.

 

[Redbelly98]

If α is the angle taken from the x-axis or horizontal, then cosα is the x-component.

If α is taken from the y-axis or vertical, then cosα is the y-component.

 

[tomcue]

Cosα can be used for both x and y components in a problem, depending on the context. In general, cosα represents the ratio of the adjacent side to the hypotenuse in a right triangle, which can be applied to both the x and y components.

For example, if we have a right triangle where the adjacent side is the x component and the hypotenuse is the overall length, then cosα would be used to calculate the x component. Similarly, if we have a right triangle where the adjacent side is the y component and the hypotenuse is the overall length, then cosα would be used to calculate the y component.

The key is to understand the geometry of the problem and identify which side is the adjacent side and which is the hypotenuse. This will determine whether cosα should be applied to the x or y component. Additionally, it is important to note that cosα can also be used in non-right triangle problems, where it represents the ratio of the adjacent side to the hypotenuse of a similar right triangle.

Overall, the use of cosα in the x or y component depends on the specific problem and its geometry. It is important to carefully analyze the problem and identify the relevant sides and angles in order to determine the appropriate use of cosα.