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

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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.
 
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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.