Simple angle relationship question

AI Thread Summary
To find the angle gamma when given angle theta in degrees and the relationship tan(theta) = C*tan(gamma), it is crucial to maintain consistent units. If theta is used in degrees, gamma must also be calculated in degrees, or vice versa if radians are used. The constant C will vary depending on the unit system, so using the same constant across different units will yield incorrect results. The calculations show that using degrees gives a different result than using radians, highlighting the importance of unit consistency. Therefore, always convert angles to the same unit before performing calculations to ensure accuracy.
jx44
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So I have a minor in mathematics yet I am confusing myself over the following - if I am given an angle, theta, in degrees and need to find a second angle, gamma, in degrees, and the relationship is tan(theta) = C*tan(gamma), where C is some constant, can I plug in theta in degrees and get gamma in degrees? Or do I need to convert theta to radians, find gamma in radians, then convert gamma to degrees again? If I do it with degrees I get 26.32, but if I do it the radians way i get 27.69.
 
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Careful, that constant is going to be different if you're using radians or degrees or arcseconds or what have you, if you just bounce around units and use the same constant, you'll be wrong
 
tan(15degrees)=(13/24)*tan(gamma)

gamma = arctan ((24/13)*tan(15 degrees))

gamma = 26.32
 
Ah, but you got the answer in radians originally, didn't you? Then you had to convert it to degrees

tan(15 degrees)=tan(.261...) they're the outright same number, that value for C will always without fail give you the answer in radians, regardless of what you use in the input
 
Thread 'Variable mass system : water sprayed into a moving container'

Thread 'Variable mass system : water sprayed into a moving container'

Starting with the mass considerations #m(t)# is mass of water #M_{c}# mass of container and #M(t)# mass of total system $$M(t) = M_{C} + m(t)$$ $$\Rightarrow \frac{dM(t)}{dt} = \frac{dm(t)}{dt}$$ $$P_i = Mv + u \, dm$$ $$P_f = (M + dm)(v + dv)$$ $$\Delta P = M \, dv + (v - u) \, dm$$ $$F = \frac{dP}{dt} = M \frac{dv}{dt} + (v - u) \frac{dm}{dt}$$ $$F = u \frac{dm}{dt} = \rho A u^2$$ from conservation of momentum , the cannon recoils with the same force which it applies. $$\quad \frac{dm}{dt}...
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