Precalculus Term 1

Brian Sterr, Nov 13, 2015

Materials for my 1st term Precalculus class at Stuyvesant High School. Textbook: Cohen, [i]Precalculus with Unit Circle Trigonometry[/i], 4th Edition.

Table of Contents

  1. Trigonometry
    1. Unit Circle Trigonometry
    2. Unit Circle: Complementary Angles
    3. Unit Circle: Sine and Cosine Functions
    4. Graphing Sine/Cosine with Translations
    5. Tangent for Acute Angles
    6. Graphing the Tangent Function
    7. Lighthouse Function p.553 #69
    8. Reciprocal Functions
    9. Inverses of Trigonometric Functions
    10. Cosine of the Difference of Two Angles
    11. The Ambiguous Case of SSA
  2. Vectors
    1. Projection of a Vector
    2. Linear Combination of Vectors
    3. Dot Product of Two Vectors
    4. Dot Product: Component Form
  3. Optimization
    1. Classwork 46 #3
  4. Polynomials
    1. Polynomial Inequality
  5. Rational Functions
    1. p.308 Example 4
    2. p.309 Example 6
    3. p.312 Example 8
    4. Rational Function with a Hole

1.

Trigonometry

  • 1. Unit Circle Trigonometry
  • 2. Unit Circle: Complementary Angles
  • 3. Unit Circle: Sine and Cosine Functions
  • 4. Graphing Sine/Cosine with Translations
  • 5. Tangent for Acute Angles
  • 6. Graphing the Tangent Function
  • 7. Lighthouse Function p.553 #69
  • 8. Reciprocal Functions
  • 9. Inverses of Trigonometric Functions
  • 10. Cosine of the Difference of Two Angles
  • 11. The Ambiguous Case of SSA

1.1.

Unit Circle Trigonometry

Drag the slider for [math]\theta[/math] to adjust the angle. Notice the coordinates of point [math]P[/math] on the unit circle.
– Brian Sterr

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1.6.

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1.7.

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1.8.

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1.9.

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1.10.

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1.11.

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2.

Vectors

  • 1. Projection of a Vector
  • 2. Linear Combination of Vectors
  • 3. Dot Product of Two Vectors
  • 4. Dot Product: Component Form

2.1.

Projection of a Vector

– Brian Sterr

2.2.

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2.4.

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3.

Optimization

  • 1. Classwork 46 #3

3.1.

Classwork 46 #3

– Brian Sterr

4.

Polynomials

  • 1. Polynomial Inequality

4.1.

Polynomial Inequality

As you drag the slider above, watch how the sign of each of the factors of [math]f\left(x\right)[/math] changes. Each factor changes signs exactly once, as you pass its critical value. This is why the roots are called critical values, because they are the [math]x[/math]-values at which the sign of the corresponding factors changes.[br][br]If you want to see what the numerical value of each factor is, then check the "Numbers" box.
– Brian Sterr

5.

Rational Functions

  • 1. p.308 Example 4
  • 2. p.309 Example 6
  • 3. p.312 Example 8
  • 4. Rational Function with a Hole

5.1.

p.308 Example 4

Example 4 from p.309[br]Done according to the directions I gave you.
– Brian Sterr

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