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

[Somefantastik]

if

[tex] \mu = cos(\theta) [/tex] and [tex] \mu_{0} = cos(\theta_{0}) [/tex]

and

[tex] cos(\pi - \Theta) = \mu_{0}\mu + \sqrt{1-\mu_{0}^{2}}\sqrt{1-\mu^{2}}cos(\phi) [/tex]

Then

[tex] cos(\pi - \Theta) = cos(\theta_{0})cos(\theta) + sin(\theta_{0})sin(\theta)cos(\phi) [/tex]


Is this not correct?

 

[g_edgar]

Is this not correct?

What if one of the sines is negative?

 

[Somefantastik]

sorry, range of [tex]\theta[/tex] is 0 to 60 degrees, and [tex] \theta_{0} [/tex] 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 [itex]\theta[/itex] and [itex]\Theta[/itex] the same variable?

(2) What is [itex]\phi[/itex]?

(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