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).

 

[Subhotosh Khan]

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).

Please follow the rules of posting in this forum, as enunciated at:

READ BEFORE POSTING

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.