Class notes

Class notes MCV4U

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Course
MCV4U

Institution
12th Grade

Calculus notes covering key concepts, formulas, and step by step examples, these notes are perfect for students looking to reinforce their understanding. Topics include, derivative and derivative rules, applications of derivatives, real world examples. Ideal for study sessions, practice questions, ...

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Uploaded on October 14, 2024
Number of pages 2
Written in 2023/2024
Type Class notes
Professor(s) Lajoy
Contains All classes

Institution Secondary school
Education 12th Grade
Course MCV4U
School year 4

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4.1 Derivatives of the Sine and Cosine Functions

Graphical reasoning can be applied to determine the exact derivative of a sinusoidal function.

Determine the derivative of sin x.
𝑥 𝑠𝑖𝑛 𝑥 𝑑
𝑑𝑦
𝑠𝑖𝑛 𝑥

0
fin co

π
I

V
2 O
π o 1
3π
2
1 0
2π
I
a) Complete the 𝑠𝑖𝑛 𝑥 column in the table.

b) Estimate the instantaneous rate of change (tangent slope) of 𝑠𝑖𝑛 𝑥 at 𝑥 = 0 using a secant line. Use the interval
0π 1π
⎡ 100 , ⎤.
⎣ 100 ⎦

I
0.999 1
c) Complete the instantaneous rate of change column.
𝑑
d) Graph the derivative function. What do you notice about the values of 𝑑𝑦
𝑠𝑖𝑛 𝑥? What is the derivative of 𝑠𝑖𝑛 𝑥?
Sina cossi
Determine the derivative of sin x.

𝑥 𝑐𝑜𝑠 𝑥 𝑑
𝑑𝑦
𝑐𝑜𝑠 𝑥

0
I
π
2
f sink
π
1 O
3π
2 O I
2π 0
a) Complete the 𝑐𝑜𝑠 𝑥 column in the table.

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