Factorising Equation for dI/dθ = 0 with I = 0.8x10^-5 and Cosine Functions

  • Thread starter kasse
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In summary, the conversation involves finding the zeros of a derivative function with a specific value, and using trigonometric identities to simplify the equation and solve for the factors.
  • #1
kasse
384
1
I want [tex]\frac{dI}{d \theta} = 0[/tex] when [tex]I = 0.8 \cdot 10^{-5}[\frac{273}{16} + \frac{17}{2}cos(kd sin \theta) + 2cos(2kd sin \theta)][/tex]

If I've calculated correctly, this means that [tex]-8.5sin(8.1sin \theta)8.1cos \theta - 32.4sin(16.2sin \theta)cos \theta = 0[/tex]. Can somebody help me factorise this?
 
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  • #2
If only the stuff in brackets is the argument of the first sine of each term, you could get away with dividing through by [tex] cos \theta [/tex] to leave you with

[tex]
-8.5sin(8.1sin \theta)8.1 - 32.4sin(16.2sin \theta) = 0
[/tex]

which is equivalent to
[tex]
-68.85sin(8.1sin \theta) - 32.4sin(16.2sin \theta) = 0
[/tex]
 
  • #3
Then recognising 16.2sinθ = 2(8.1sinθ) we can apply the sin double angle formula (sin2α = 2cosαsinα) on the second term
 

1. What is dI/dθ?

dI/dθ is the derivative of the function I with respect to the variable θ. In other words, it represents the rate of change of I with respect to θ.

2. What does it mean for dI/dθ = 0?

When dI/dθ = 0, it means that the function I is not changing with respect to θ. This can also be interpreted as the function reaching a maximum or minimum value at that specific point.

3. How do you factorise an equation for dI/dθ = 0 with I = 0.8x10^-5?

To factorise an equation for dI/dθ = 0, you will need to use the given value of I and solve for θ. This will give you a specific value for θ, which can then be used to factorise the equation.

4. What are cosine functions?

Cosine functions are a type of mathematical function that relates the input value (usually an angle) to the output value (the ratio of two sides of a right triangle). They are commonly used in trigonometry, geometry, and physics to describe periodic motion or oscillation.

5. How do cosine functions relate to factorising equations for dI/dθ = 0?

In the context of factorising equations for dI/dθ = 0, cosine functions can be used to represent the function I in terms of θ. This allows for the equation to be solved for specific values of θ, which can then be used to find the maximum or minimum value of the function I.

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