MHB Where does radius sin angle sin rotation come from?

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The discussion centers on the derivation of the formula for calculating a new "x" point of rotation, specifically the term "radius sin angle sin rotation." The formula is derived using the angle difference identity for cosine, which states that cos(α - β) = cos(α)cos(β) + sin(α)sin(β). A participant notes a potential issue with a minus sign in the formula. Ultimately, the original poster finds clarity through a reference to a Wikipedia article. The conversation highlights the importance of understanding trigonometric identities in rotation calculations.
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For calculating a new "x" point of rotation I found the formula:

x' = radius * cos(angle + -rotation) which converts to:

x' = radius cos angle cos rotation - radius sin angle sin rotation

Where does "radius sin angle sin rotation" come from?

Jerry D.
 
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jerryd said:
For calculating a new "x" point of rotation I found the formula:

x' = radius * cos(angle + -rotation) which converts to:

x' = radius cos angle cos rotation - radius sin angle sin rotation

Where does "radius sin angle sin rotation" come from?

Jerry D.

Hi jerryd! Welcome to MHB! ;)

It appears we're applying the angle difference identity for the cosine:
$$\cos(\alpha - \beta) = \cos\alpha \cos\beta + \sin\alpha \sin\beta$$
See for instance wiki.

However, we do seem to have a problem with a minus sign... (Worried)
 
Thanks for the reply.

The link to Wiki answered everything.

Jerry D.
 
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