Are these the correct cos and sin relations for the given values?

[Somefantastik]

if

$$\mu = cos(\theta)$$ and $$\mu_{0} = cos(\theta_{0})$$

and

$$cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi)$$

Then

$$cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi)$$


Is this not correct?

 

[g_edgar]

Is this not correct?

What if one of the sines is negative?

 

[Somefantastik]

sorry, range of $$\theta$$ is 0 to 60 degrees, and $$\theta_{0}$$ range is 0 to 70 degrees. As far as I can tell, sin will always be positive. But regardless, sin(theta)< 0 would change the value of the over all equation, but are the two equations not equal?

 

[Elucidus]

Several questions:

(1) Are $\theta$ and $\Theta$ the same variable?

(2) What is $\phi$?

(3) I'm not sure what the equation is getting at. It appears to be a hyrid of a cofunction, symmetric, and angle sum identity. Something feels missing. Could you provide more detail as to what you are trying to show here?

--Elucidus

 

[Integral]

Yes, your final relationship follows from what you have given.

 

[Somefantastik]

Ok thanks Integral; I just wanted to make sure I wasn't crazy