April 4th 2011 Julia Csath Topic: The derivative of the Sine function
Overview:
Today in class was Heather's day to teach. We started off class with a graph that had both a sine function and a cosine function graphed on the same axis. It was our task to come up with everything we could think of that had to do with the sine or cosine functions. After that in our table groups we received an envelope filled with functions and their derivatives and we had to determine which graphs belonged together. Once that was over we looked at the graph of the sine function and had to determine what its derivative looked like.
Notes:
Where is the instantaneous rate of change: Zero?
Increasing?
Decreasing?
Highest?
Lowest?
Instantaneous rate of change ............................................................................ f(x)= sin x
0 - π/2
decreasing
π /2
0
π/2 - π
decreasing
π
lowest
π - 3π/2
increasing
3π/2
0
3π/2 - 2π
increasing
2π
highest
f ' (x)= cos x
cos x
*the derivative of the sine function is the cosine function*
Homework: Work on the derivatives of trig functions worksheet.
April 6th 2011 Julia Csath Topic: Presentations of Construction Company Proposals Overview: Today in class we presented our proposals for the construction company’s assignment. They were all very entertaining and I believed aided in the discussion as to whether or not to take the contract.
Homework: Continue to work on the derivatives of trig functions worksheet.
Other Trig Derivatives Emily Brant April 8,2011
1. Determine d(tanx)
dx
*rewrite to
y=sinx
cosx
*solve for the derivative
y’=(cosx)(cosx)-(-sinx)(sinx)
cos2x
y’=cos2x+sin2x
cos2x
y’= 1
cos2x
y’=sec2x
2. Determine d(cotx)
dx
*rewrite as
y=cosx
sinx
*solve for the derivative
y’=(-sinx)(sinx)-(cosx)(cosx)
sin2x
y’=-sin2x-cos2x
sin2x
y’= 1
sin2x
y’=-csc2x
3. Determine d(secx)
dx
*rewrite as
y= 1
cosx
*solve for derivative
y’=(0)(cosx)-(1)(-sinx)
cos2x
y’= sinx
cos2x
*Break that up to:
sinx . 1
cosx cosx
*that equals
y’=tanxsecx
4. Determine d(cscx)
dx
*rewrite as
y= 1
sinx
*solve for derivative
y’=(0)(sinx)-(1)(cosx)
sin2x
y’=-cosx
sin2x
*break that up into:
-cosx . 1
sinx sinx
*which equals
y’=-cotxcscx
Gurpriya Kaberwal April 11, 2011 Applications of Trig functions Today in class, we did some group work even though it wasn’t a Tuesday. We started off by getting into groups of 4-5. Then we were asked to work within our groups and sort out several pieces with equations of trig functions on them and then further divide them two more times to end with three sets of functions . Each group then presented the ideas and strategies they used to sort the functions out. For example, some groups sorted the functions by checking if the functions were sine or cosine, whether the functions were solvable using the chain rule, what kind of transformations they had, etc. Problem solving strategies: · List our givens · Draw a picture/diagram/sketch · Come up with function/equation · Find max/min points, inc/dec intervals, inflection points · Use the first and second derivative tests *(make sure the values are in the interval) · Check if the answer makes sense
After figuring out these above mentioned strategies to solve questions involving trig functions and derivatives, we solved some examples together as a class ( on the handout “applications of trig derivatives”).
Today was a work period in preparation for the upcoming test. The homework includes the Derivatives of Trig Functions worksheet and the Review/Practice Test booklet.
Today was a work period and so we got a chance to work on the review package and the practice test for Chapter 4. We also got a chance to study for the upcoming test and ask Gillian for help. Test (quest) on Chapter 4: Derivatives of Sinusoidal Functions is on Friday, April 15, 2011. Here are some links that would help you review for the test! Good Luck!
Julia Csath
Topic: The derivative of the Sine function
Overview:
Today in class was Heather's day to teach. We started off class with a graph that had both a sine function and a cosine function graphed on the same axis. It was our task to come up with everything we could think of that had to do with the sine or cosine functions. After that in our table groups we received an envelope filled with functions and their derivatives and we had to determine which graphs belonged together. Once that was over we looked at the graph of the sine function and had to determine what its derivative looked like.
Notes:
Where is the instantaneous rate of change: Zero?
Increasing?
Decreasing?
Highest?
Lowest?
Instantaneous rate of change
f ' (x)= cos x
*the derivative of the sine function is the cosine function*
Homework: Work on the derivatives of trig functions worksheet.
April 6th 2011
Julia Csath
Topic: Presentations of Construction Company Proposals
Overview:
Today in class we presented our proposals for the construction company’s assignment. They were all very entertaining and I believed aided in the discussion as to whether or not to take the contract.
Homework: Continue to work on the derivatives of trig functions worksheet.
Other Trig Derivatives
Emily Brant
April 8,2011
1. Determine d(tanx)
dx
*rewrite to
y=sinx
cosx
*solve for the derivative
y’=(cosx)(cosx)-(-sinx)(sinx)
cos2x
y’=cos2x+sin2x
cos2x
y’= 1
cos2x
y’=sec2x
2. Determine d(cotx)
dx
*rewrite as
y=cosx
sinx
*solve for the derivative
y’=(-sinx)(sinx)-(cosx)(cosx)
sin2x
y’=-sin2x-cos2x
sin2x
y’= 1
sin2x
y’=-csc2x
3. Determine d(secx)
dx
*rewrite as
y= 1
cosx
*solve for derivative
y’=(0)(cosx)-(1)(-sinx)
cos2x
y’= sinx
cos2x
*Break that up to:
sinx . 1
cosx cosx
*that equals
y’=tanxsecx
4. Determine d(cscx)
dx
*rewrite as
y= 1
sinx
*solve for derivative
y’=(0)(sinx)-(1)(cosx)
sin2x
y’=-cosx
sin2x
*break that up into:
-cosx . 1
sinx sinx
*which equals
y’=-cotxcscx
Gurpriya Kaberwal
April 11, 2011
Applications of Trig functions
Today in class, we did some group work even though it wasn’t a Tuesday. We started off by getting into groups of 4-5. Then we were asked to work within our groups and sort out several pieces with equations of trig functions on them and then further divide them two more times to end with three sets of functions . Each group then presented the ideas and strategies they used to sort the functions out. For example, some groups sorted the functions by checking if the functions were sine or cosine, whether the functions were solvable using the chain rule, what kind of transformations they had, etc.
Problem solving strategies:
· List our givens
· Draw a picture/diagram/sketch
· Come up with function/equation
· Find max/min points, inc/dec intervals, inflection points
· Use the first and second derivative tests *(make sure the values are in the interval)
· Check if the answer makes sense
After figuring out these above mentioned strategies to solve questions involving trig functions and derivatives, we solved some examples together as a class ( on the handout “applications of trig derivatives”).
Home work: question # 3 (back of the handout)
Useful links:
· http://www.intmath.com/differentiation-transcendental/4-applications-derivatives-trigonometric.php
Work Period
Connor Dorval
April 12, 2011
Today was a work period in preparation for the upcoming test. The homework includes the Derivatives of Trig Functions worksheet and the Review/Practice Test booklet.
Useful Resources:
Summary of Trig Derivatives- http://www.math.uwo.ca/~rnbryan/Al's_trig_derivatives.pdf
A walkthrough of several examples- http://www.youtube.com/watch?v=xJ3C_pZssJI&feature=related
A...differerent...way of explaining examples- http://www.youtube.com/watch?v=rd4DCmB2l4Y&feature=related
Talha Sadiq
April 13, 2011
Work Period
Today was a work period and so we got a chance to work on the review package and the practice test for Chapter 4. We also got a chance to study for the upcoming test and ask Gillian for help. Test (quest) on Chapter 4: Derivatives of Sinusoidal Functions is on Friday, April 15, 2011. Here are some links that would help you review for the test! Good Luck!
http://www.sosmath.com/calculus/diff/der03/der03.html
http://people.hofstra.edu/stefan_waner/trig/trig3.html
http://www.intmath.com/differentiation-transcendental/4-applications-derivatives-trigonometric.php
Homework:
Complete the review package & practice test! Study hard for the test this Friday!
Jennifer Taylor
April 15, 2011
Math Quest Today on Chapter 4: Derivatives of Sinusoidal Functions!
Upcoming Monday we start Exponential and Logarithmic functions. Keeping reviewing!