20100729 Thu

Covered sections 5.4, 5.5, 5.6. Also discussed a little bit of asymptotes again, as well as emphasized determining the domain and range of functions. In particular, I discussed the domain and range of inverse functions.

Key Concepts:
Section 5.4
pg 465 Definition: Tangent, Cotangent, Secant, and Cosecant Functions
pg 465 Identities from the Definitions
Section 5.5
pg 477 Definition: The Inverse Sine Function
pg 479 Definition: The Inverse Cosine Function
pg 480 Inverses of Tangent, Cotangent, Secant, and Cosecant
pg 481 Function Gallery
pg 482 Identities for the Inverse Functions
Section 5.6
pg 490 Thoerem: Trigonometric Functions of an Acute Angle of a Right Triangle

Homework:
Section 5.4 1-89, every 8; Also 2, 3-28 ("Undefined" is a possible answer),
Section 5.5 1-97, every 8; Skip 49, 57, 81, 89; Also 65-79 Odd, 93-98
Section 5.6 1-57, every 8
Due Monday

[20100805]
I might have learned on this day that the signs of Sin(x), Cos(x), and Tan(x) in quadrants I, II, III, and IV, can be given by ASTC (All Students Take Calculus). That is "All" are positive, only "Sine" is positive, only "Tangent" is positive, and finally only "Cosine" is positive, in quadrants I, II, III, and IV, respectively.

20100728 Wed

Covered sections 5.1, 5.2, 5.3
Also reviewed solving inequalities

Key Concepts:
Section 5.1
pg 422 Degree-Radian Conversion
pg 425 Theorem: Length of an Arc
pg 427 Theorem: Linear Velocity in Terms of Angular Velocity
Section 5.2
pg 434 Definition: Sine and Cosine
pg 441 The Fundamental Identity of Trigonometry
Section 5.3
pg 448 Definition: Periodic Function
pg 449 Definition: Amplitude
pg 453 Theorem: Period of y = sin(Bx) and y = cos(Bx)
pg 453 The General Sine Wave
pg 456 Definition: Frequency

Homework:
Section 5.1 1-97, every 8 (i.e. 1, 9, 17, ...)
Section 5.2 1-89, every 8
Section 5.3 1-73, every 8
Due Monday

20100727 Tues

Covered sections 4.3, 4.4

Key Concepts:
Section 4.3
pg 387 Rules of Logarithms with Base a
pg 389 Base-Change Formula
Section 4.4
pg 399 STRATEGY: Solving Exponential and Logarithmic Equations

Homework:
Section 4.3 1-89, every 8
Section 4.4 1-81, every 8
Due Monday

Extra Credit Homework
1) Copy all brown and green boxes, 2) Copy and work through examples, 3) Try This for Sections P.1, P.2, P.3, P.5, 1.1, 2.4, 2.5, 3.6.
1) Copy all brown and green boxes for Sections 1.6, 2.1, pg 220

[20100728]

20100726 Mon

Covered sections 4.1, 4.2

Key Concepts:
Section 4.1
pg 354 Definition: Exponential Function
pg 358 Properties of Exponential Functions
pg 360 One-to-One Property of Exponential Functions
pg 362 Compound Interest Formula
pg 363 Continuous Compounding Formula
Section 4.2
pg 370 Definition: Logarithmic Function
pg 372 Properties of Logarithmic Functions [compare this with pg 358 Properties of Exponential Functions]
pg 374 One-to-One Property of Logarithms

Homework:
Section 4.1 1-85, every 4
Section 4.2 1-101, every 4
Due Monday

[20100728]