PreCalculus
Chapter 1
Unit 1-1 Analytic Trigonometry
- Standard 1a: Draw angles that are negative or are larger than 180°
- Standard 1b: Find the quadrant and reference angles of a given angle in
standard position.
- Standard 1c: Given a point or trig function value and quadrant of the terminal side of an angle, find the exact value of all the trigonometric functions of the angle.
Outline
- Screencast Review: Angles on the x-y plane
- Positive & Negative Angles
- Co-terminal Angles
- Angles in Standard Position
- Six trigonometric functions of an angle
- Desmos Activity
- Assignment 1-1: Pg. 9 All
Unit 1-2 The Unit Circle and Special Triangles
- Standard 1d: Convert between radians and degrees.
- Standard 1e: Apply 30-60-90 and 45-45-90 triangle dimensions to the unit circle
- Standard 1f: Use exact values from the special triangles to simplify trigonometric expressions
Outline
- Radian measure of an angle
- How did radians come about?
- How do we convert between radians and degrees?
- Special Triangles and the Unit Circle
- Special Angles and Trigonometric Expressions
- Assignment 1-2: Part A Pg 15 #1-9 Part B Pg 15 #10-16
Unit 1-3 Reference Angles & The Graphing Calculator
- Standard 1g: Use a calculator to find approximate trigonometric values for a given angle and approximate angle values for a given trigonometric value.
Outline
- What the calculator tells you
- sin-1 and tan-1 angles are in QI and IV
- cos-1 angles are in QI and II
- Using Reference Angles to...
- Find values of an angle given its sine value
- Find values of an angle given its cosine value
- Find values of an angle given its tangent value
- Giving all possible values for an angle
- Degree measure ±360n
- Radian Measure ±2πn
- Finding Inverse Reciprocal Values (sec-1, csc-1, & cot-1 buttons aren't on the TI-84)
- Assignment 1-3: Pg 21 #1-15
Unit 1-4 Vectors
- Standard 1h: Find and draw a resultant vector from other component vectors..
- Standard 1i: Find the direction angle of a resultant vector from other component vectors.
- Standard 1j:Model and solve problems involving vectors
Outline
- Vectors versus Line Segments
- Direction
- Magnitude (Size)
- Adding and Subtracting Vectors
- Using Trigonometric Functions with Vectors
- Cosine & the x-component
- Sine & the y-component
- Using Cosine to Find the Direction of a Vector
- Modelling Vector Problems
- Assignment 1-4:Pg 32 Part A #1-8, 13-16 Part B #17-23