Use the definitions of the reciprocal trigonometric functions (along with the Pythagorean theorem) to establish the identities given in the questions below.
Page 334–335 questions 34, 39, 40
Models with Trigonometric Functions
Here’s the question we considered in today’s lesson. See how far you can get on this question tonight, and we’ll continue our discussion tomorrow.
The London Eye is 15 m off the ground, and has a diameter of 120 m. The London Eye completes one revolution every 30 minutes.
- Develop a function to model the height of a passenger on the London Eye t minutes after boarding a capsule.
- How far above ground would passengers in a capsule be after
a. 10 minutes have passed?
b. 25 minutes have passed?
Calculus (Option Topics) Test 1 [Updated]
We’ll have our first test on the Calculus Option topics on Sunday, March 6th.
This test will cover material that includes differential equations, important theorems and definitions in Calculus (Rolle’s Theorem, the Mean Value Theorem, continuity and differentiability, etc.), and l’Hôpital’s Rule.
Update: The following questions will be useful.
page 1471–1474 questions 1, 4, 10, 16, 19, 22–27
page 1436 questions 9, 17
page 1354 questions 4, 6, 14, 15
Euler’s Method Homework Assignment
Complete the questions on this PDF file for the beginning of class on Wednesday, March 2nd.
Euler’s Method [Updated]
You should now have received an email with a list of questions. Complete questions 4, 7, and 14 for tomorrow’s class.
Update: note that there’s an error in question 14: \(y(2)\), rather than \(y(3)\), should appear in part c).
Logarithms Test
We’ll have a test on logarithms on Thursday, February 25th.
The following questions will be useful for revision, and we can discuss any difficulties with these in class on Wednesday.
Page 243–245 questions 2, 4, 7, 8, 14, 16–19, 21–25
Logarithms
Complete the following question for tomorrow’s lesson.
If you can earn 5% interest compounded quarterly, how long will it take for your investment to double in value? Find an exact expression for your answer, with time measured in years.
[Note that \(\ln 2\) is an exact expression, and may appear in a correct solution to this question.]Homogeneous Differential Equations
Complete page 1470 questions 25 and 27. You will find it helpful to simplify expressions as much as possible in your intermediate steps.
Logarithms Homework
Complete the following questions for our next lesson. These are all relatively short, so you should be able to complete all questions for our lesson on Monday.
Pages 232–233 questions 3, 5, 12, 15, 18, 20, 21, 26, 31, 33, 44, 47, 48, 54, 56, 57, 60, 61, 63, 67, 69, 71, 72–77, 79, 80, 84
Induction and the Binomial Theorem Test
We’ll have a test on mathematical induction and the Binomial Theorem on Monday, February 8th.
To prepare for the test, complete p. 203–205 questions 20, 22, 24, 28, 26, 45, 47
We will discuss these questions in Thursday’s lesson.