Where does radius sin angle sin rotation come from?

[jerryd]

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.

 

[I like Serena]

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)

 

[jerryd]

Thanks for the reply.

The link to Wiki answered everything.

Jerry D.