Quick Guide To The Precalculus Tasks
Quick Guide to the Precalculus Tasks Task 1
A. Define the six trigonometric functions, including diagrams
1. Right triangle definitions.
Section 5.2
2. Unit circle definitions.
Section 5.3
3. Explain the relationship.
Sections 5.2 and 5.3
a. Explain memory tricks for trig.
Section 5.2
This task comes almost directly from the text with a supporting sentence or two about how values from regular and right triangle are similar or different. Task 2
A. Write the Pythagorean identities.
Section 5.2
This part comes directly from the text.
B. Prove a trigonometric identity.
Section 6.1, Example 5
Some students work with this proof as if it were an equation, changing both sides of the proof statement until they arrive at the conclusion. Instead, students should work with just one side of the statement and show algebraically that it can be transformed to equal the other side of the statement. Proving a formula involves carefully breaking it down to the smallest possible steps and justifying each step with a rule or axiom from arithmetic, algebra, or trigonometry. Task 4
Given: y =
A cos( Bx
C
) +
D
and data about depth and time of tides, model the problem and apply the model.
Section 5.5, Example 9, possibly Example 6
For the part where students must find a range of safe values for the last part of the task, some students incorrectly find the only first safe time to dock the boat, instead of the full range of times when it is safe to dock the boat. Purely graphical solution methods are acceptable if carefully illustrated and explained. Purely algebraic solution methods are also acceptable if all steps are justified and the “other answer” for the inverse cosine is carefully explained. Task 3
A1. Explain how the complex numbers extend the real numbers.
Section 1.4
A2. Explain the parts of a complex number.
Section 1.4
A3a. Explain complex number addition using symbols and using
A. Define the six trigonometric functions, including diagrams
1. Right triangle definitions.
Section 5.2
2. Unit circle definitions.
Section 5.3
3. Explain the relationship.
Sections 5.2 and 5.3
a. Explain memory tricks for trig.
Section 5.2
This task comes almost directly from the text with a supporting sentence or two about how values from regular and right triangle are similar or different. Task 2
A. Write the Pythagorean identities.
Section 5.2
This part comes directly from the text.
B. Prove a trigonometric identity.
Section 6.1, Example 5
Some students work with this proof as if it were an equation, changing both sides of the proof statement until they arrive at the conclusion. Instead, students should work with just one side of the statement and show algebraically that it can be transformed to equal the other side of the statement. Proving a formula involves carefully breaking it down to the smallest possible steps and justifying each step with a rule or axiom from arithmetic, algebra, or trigonometry. Task 4
Given: y =
A cos( Bx
C
) +
D
and data about depth and time of tides, model the problem and apply the model.
Section 5.5, Example 9, possibly Example 6
For the part where students must find a range of safe values for the last part of the task, some students incorrectly find the only first safe time to dock the boat, instead of the full range of times when it is safe to dock the boat. Purely graphical solution methods are acceptable if carefully illustrated and explained. Purely algebraic solution methods are also acceptable if all steps are justified and the “other answer” for the inverse cosine is carefully explained. Task 3
A1. Explain how the complex numbers extend the real numbers.
Section 1.4
A2. Explain the parts of a complex number.
Section 1.4
A3a. Explain complex number addition using symbols and using