Turning Points with sin and cos

Anthonyk2013

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Wondering if I'm on the right track. Following examples in a book so not sure if my method is right.
 

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Wondering if I'm on the right track. Following examples in a book so not sure if my method is right.
It seems ok so far. If the redish θ=0\displaystyle \theta\, = \, 0^\circ and θ=360\displaystyle \theta\, = \, 360^\circ represent the domain of the function, the 157.39\displaystyle ^\circ is one+ solution for the derivative equal to zero [actually I get 157.380\displaystyle ^\circ]. Note though that you need to check that the second derivative isn't zero* to see if it is a turning point.



*More generally, check that the first non-zero derivative after the first is an even derivative.


+EDIT: (changed for 'the') Thnx Subhotosh Khan for point that out, I had missed that.
 
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The redish represent to range. Question in full attached.
 

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There is a second solution:

Θ = 180° + 157.380°
 
Aside from what Ishuda told you, the only advice I have is to try and write explicitly what you mean. For instance, at first I couldn't tell what the two theta equals statements in red meant. I would have written something like:

θ[0,360]\displaystyle \theta \in \left[0^{\circ },360^{\circ }\right]

Additionally, when first taking the derivative, you wrote dy/dx. Taking the derivative of y with respect to x would result in 0, as there is no x in the expression. Now, it might seem like I'm just nitpicking and being overly critical, but establishing these practices will help you immensely later on. When you start working with more complex equations with more than two variables and/or using u-substitution, being clear about what variables you're derivating or integrating with respect to is very important. If you're not careful, you can end up with a totally wrong answer because of poor notation.
 
Aside from what Ishuda told you, the only advice I have is to try and write explicitly what you mean. For instance, at first I couldn't tell what the two theta equals statements in red meant. I would have written something like:

θ[0,360]\displaystyle \theta \in \left[0^{\circ },360^{\circ }\right]

Additionally, when first taking the derivative, you wrote dy/dx. Taking the derivative of y with respect to x would result in 0, as there is no x in the expression. Now, it might seem like I'm just nitpicking and being overly critical, but establishing these practices will help you immensely later on. When you start working with more complex equations with more than two variables and/or using u-substitution, being clear about what variables you're derivating or integrating with respect to is very important. If you're not careful, you can end up with a totally wrong answer because of poor notation.

Thanks. Bad habits. Been trying to eliminate those errors.
 
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