Differentiation

[Derrickkhoo]

How to do this?
Given a trigonometric function, f(θ) = cos(θ) + sin(θ).

• Evaluate the first and second derivative for f(θ).
• Produce a table for f(θ), f’’(θ), and f’’(θ) in the range of 0 to 360 degrees. Then, use 15 degrees interval for each dataset in the set of {0, 15, 30, …, 345, 360}.
• Draw three graphs to represent f(θ), f’’(θ), and f’’(θ) using the datasets in Question 2(b).

 

[Deleted member 4993]

How to do this?
Given a trigonometric function, f(θ) = cos(θ) + sin(θ).

• Evaluate the first and second derivative for f(θ).
• Produce a table for f(θ), f’’(θ), and f’’(θ) in the range of 0 to 360 degrees. Then, use 15 degrees interval for each dataset in the set of {0, 15, 30, …, 345, 360}.
• Draw three graphs to represent f(θ), f’’(θ), and f’’(θ) using the datasets in Question 2(b).

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Please share your work/thoughts about this assignment

Hint:

$\displaystyle \frac{d}{d\theta}\left[sin(\theta)\right] \ = cos(\theta)$

 

[HallsofIvy]

I presume you are just beginning Calculus. The rules you need are

If $\displaystyle f(\theta)= u(\theta)+ v(\theta)$ then $\displaystyle f'(\theta)= u'(\theta)+ v'(\theta)$, $\displaystyle f''(\theta)= u''(\theta)+ v''(\theta)$ and $\displaystyle f'''(\theta)= u'''(\theta)+ v'''(\theta)$

as well as $\displaystyle (sin(\theta))'= cos(\theta)$ and $\displaystyle (cos(\theta))'= -sin(\theta)$. Of course the "second derivative" is just the derivative of the first derivative so repeat.