Convert 105 degrees to radians Convert 5 π 9 to radians What is the range of the equation y 2 4cos3x 7 π 12 100 degrees 2 6 Derivatives of Trigonometric Functions Lesson 35 Objectives ID: 324277
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Slide1
Drill
Convert 105 degrees to radiansConvert 5π/9 to radiansWhat is the range of the equation y = 2 + 4cos3x?
7
π
/12
100 degrees
[-2, 6]Slide2
Derivatives of Trigonometric Functions
Lesson 3.5Slide3
Objectives
Students will be able touse the rules for differentiating the six basic trigonometric functions.Slide4
Find the derivative of the sine function.Slide5
Find the derivative of the sine function.Slide6
Find the derivative of the cosine function.Slide7
Find the derivative of the cosine function.Slide8
Derivatives of Trigonometric FunctionsSlide9
Example 1 Differentiating with Sine and Cosine
Find the derivative.Slide10
Example 1 Differentiating with Sine and Cosine
Find the derivative.Slide11
Example 1 Differentiating with Sine and Cosine
Find the derivative.Slide12
Example 1 Differentiating with Sine and Cosine
Find the derivative.Slide13
Example 1 Differentiating with Sine and Cosine
Find the derivative.
Remember that cos
2
x + sin
2
x = 1
So sin x = 1 –
cos
2
xSlide14
Example 1 Differentiating with Sine and Cosine
Find the derivative.Slide15
Homework, day #1
Page 146: 1-3, 5, 7, 8, 10On 13 – 16Velocity is the 1st derivativeSpeed is the absolute value of velocityAcceleration is the 2nd derivative Look at the original function to determine motionSlide16
Find the derivative of the tangent function.Slide17
Find the derivative of the tangent function.Slide18
Derivatives of Trigonometric FunctionsSlide19
Derivatives of Trigonometric FunctionsSlide20
More Examples with Trigonometric Functions
Find the derivative of y.Slide21Slide22
More Examples with Trigonometric Functions
Find the derivative of y.Slide23Slide24
Whatta
Jerk! Jerk is the derivative of acceleration. If a body’s position at time t is s(t), the body’s jerk at time t
is Slide25
Example 2 A Couple of Jerks
Two bodies moving in simple harmonic motion have the following position functions: s1(t) = 3cos t
s
2
(t) = 2sin
t
– cos
t
Find the jerks of the bodies at time
t
.
velocity
accelerationSlide26
Example 2 A Couple of Jerks
Two bodies moving in simple harmonic motion have the following position functions: s1(t) = 3cos t
s
2
(t) = 2sin
t
– cos
t
Find the jerks of the bodies at time
t
.
velocity
acceleration
jerkSlide27
Example 2 A Couple of Jerks
Two bodies moving in simple harmonic motion have the following position functions: s1(t) = 3cos t
s
2
(t) = 2sin
t
– cos
t
Find the jerks of the bodies at time
t
.
velocity
acceleration
jerkSlide28
Homework, day #2
Page 146: 4, 6, 9, 11, 12, 17-20, 22 28, 32