How to pick theta while resolving vector.

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Choosing the correct angle (theta) when resolving a vector depends on the reference point used for the angle. The radial component can be calculated using Xcosθ if the angle is measured from the radius, while Xsinθ is used if the angle is measured from the tangent. The key is to consistently apply the appropriate trigonometric function based on the chosen angle. The magnitude of the component is important, but the sign must also be considered based on the context. Understanding these principles will help clarify the confusion around selecting theta.
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how to pick theta (angle between the vector and the component) above two which one is the right choice. I'm confused regarding choosing (theta).. what are the criteria that to be considered while choosing the angle.

from the above with my choice of theta the component changes hence the equations.

please help me :)
 
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It looks like you are trying to find the radial or the tangential component of some vector. It doesn't matter which angle you use, as long as you use the correct trig function to find the component. If you use the angle with respect to the radius, then the radial component will be Xcosθ; but if you use the angle with respect to the tangent, then the radial component will be Xsinθ. (I'm only concerned with the magnitude of the component; you'll need to add the correct sign, of course.)
 

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