Chapter 5 â Trigonometric Functions
Chapter 5 – Trigonometric Functions Section 5.1 Graphs of Sine, Cosine and Tangent Learning Goals: By the end of this lesson I will be able to sketch the graphs of f(x) = sinx , f(x) = cosx, and f(x) = tanx where x is in radian measure and determine and describe some of their key properties.
The graphs of sine, cosine and tangent are periodic (______________) Sine and Cosine graphs have an amplitude (___) of _____ and period ( ___) of _____.
Symmetric about the origin ______________________ (_____________________)
Symmetric about the origin ______________________ (_____________________)
The graph of tangent has _____ amplitude because there are no ________________. Since ____________, tan has zeros wherever
_________________
Tan has VAs where ___________________.
Transformations: the most general form:
______________________________________________
1. “___” is the amplitude (vertical stretch or compression)
2. “___” related to the period (must be factored out!!!!!!!)
3. “___” is the phase shift (horizontal left or right)
4. “___” is related to the horizontal axis of symmetry, vertical translation
Section 5.2 Graphs of Reciprocal Functions Learning Goals: By the end of this lesson I will be able to graph reciprocal trigonometric functions using primary trigonometric functions for angles in radians and determine and describe their key properties.
Note: _______ means the recipricol of sinx. Ie. __________________________
Note: _______ means the inverse function of sinx. Ie. __________________________
5.3 Transformation of Trig Function Learning Goals: By the end of this lesson I will be able to 1. Determine the amplitude, period, phase shift and vertical displacement of sinusoidal functions and sketch their graph by applying transformations. 2. Represent a sinusoidal function with an equation given its graph or its properties.
The general transformation has the form _____________________________ 1. “a” _____________________________ 2. “k” _____________________________ 3. “d” _____________________________ 4. “c” ______________________________
5.4 Solving Trigonometric Equations Learning goals: By the end of this lesson I will be able to: 1.
Solve problems involving trigonometric functions using a given graph or by generating a graph from a table of values or from its equation.
2.
Solve linear and quadratic trigonometric equations for the domain of real values between 0 and 2π and solve related problems.
When solving trigonometric equations, we are finding _______ values of _____ within a given domain. If no domain is given, there are infinite solutions because these types of functions are __________. Example1. Solve for x in
Example 2: Solve
Example 3: Solve
Example 4: Solve
Example 5: Solve
The graphs of sine, cosine and tangent are periodic (______________) Sine and Cosine graphs have an amplitude (___) of _____ and period ( ___) of _____.
Symmetric about the origin ______________________ (_____________________)
Symmetric about the origin ______________________ (_____________________)
The graph of tangent has _____ amplitude because there are no ________________. Since ____________, tan has zeros wherever
_________________
Tan has VAs where ___________________.
Transformations: the most general form:
______________________________________________
1. “___” is the amplitude (vertical stretch or compression)
2. “___” related to the period (must be factored out!!!!!!!)
3. “___” is the phase shift (horizontal left or right)
4. “___” is related to the horizontal axis of symmetry, vertical translation
Section 5.2 Graphs of Reciprocal Functions Learning Goals: By the end of this lesson I will be able to graph reciprocal trigonometric functions using primary trigonometric functions for angles in radians and determine and describe their key properties.
Note: _______ means the recipricol of sinx. Ie. __________________________
Note: _______ means the inverse function of sinx. Ie. __________________________
5.3 Transformation of Trig Function Learning Goals: By the end of this lesson I will be able to 1. Determine the amplitude, period, phase shift and vertical displacement of sinusoidal functions and sketch their graph by applying transformations. 2. Represent a sinusoidal function with an equation given its graph or its properties.
The general transformation has the form _____________________________ 1. “a” _____________________________ 2. “k” _____________________________ 3. “d” _____________________________ 4. “c” ______________________________
5.4 Solving Trigonometric Equations Learning goals: By the end of this lesson I will be able to: 1.
Solve problems involving trigonometric functions using a given graph or by generating a graph from a table of values or from its equation.
2.
Solve linear and quadratic trigonometric equations for the domain of real values between 0 and 2π and solve related problems.
When solving trigonometric equations, we are finding _______ values of _____ within a given domain. If no domain is given, there are infinite solutions because these types of functions are __________. Example1. Solve for x in
Example 2: Solve
Example 3: Solve
Example 4: Solve
Example 5: Solve
