# Differentiation

#### Derrickkhoo

##### New member
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

##### Super Moderator
Staff member
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

##### Elite Member
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.