Course Number: MS101

Course Title: Algebra and Trigonometry

STUDENT LEARNING OUTCOMES

General
 


Students will be able to model and solve equations involving exponential, logarithmic and trigonometric expression

Specific 

Students will be able to:

1. Work with Exponential Functions

    Evaluate exponential expressions by hand and using technology.
    Identify the parameters of an exponential function.
    Identify transformations of exponential functions.
    Graph exponential functions
    Define the number e.
    Calculate interest amounts using compound interest.
    Calculate interest amounts using continuous compounding.

    Recognize that a function is growing/decaying exponentially.

2. Work with Logarithmic Functions

    Define the meaning of the logarithm base a
    Evaluate logarithmic expressions by hand and using technology.
    Understand the properties of logarithms.
    Graph logarithmic functions.
    Recognize transformations of logarithmic functions.
    Use the change of base formula.
    Use the properties of logarithms to expand logarithmic expressions.
    Use the properties of logarithms to condense logarithmic expressions.
    Explain the inverse relationship between exponential and logarithms.

3. Work with Equations involving exponentials and Logarithms

    Use logarithms to solve exponential equations.
    Use exponentials to solve logarithmic equations.

4. Work with Exponential and Logarithmic Models

    Given several data points, model an exponential growth function.
    Given several data points, model and exponential decay function.
    Find the doubling time of an exponential growth function.
    Find the half-life of an exponential decay function.
    Use exponentials and logarithms to solve interest problems.

5. Work with Angles and Triangle

    Describe angles
    Use degree measure
    Use radian measure
    Sketch angles in standard position
    Convert between degree and radian measure
    Convert between decimal degrees and deg/min/sec format
    Determine if two angles are co-terminal
    Use the Pythagorean Theorem to find missing sides of triangles
    Determine if a triangle is a right triangle
    Sketch a triangle given any two sides
    Find the six trigonometric ratios of the acute angles in a right triangle
    Construct a 30-60-90 and 45-45-90 triangle from memory
    Use technology to find trigonometric ratios of angles using degrees/radians.
    Find a missing side of a right triangle using a trigonometric ratio
    Model physical situations using right triangles.

6. Work with Trigonometric Ratios

    Define the six trigonometric ratios for angles of any measure, i.e. non-acute angles
    Given a point on the terminal ray of an angle, find the trigonometric rations of the angle.
    Describe and sketch the unit circle
    Define a reference angle
    Find the reference angle of a given angle
    Evaluate, by hand, the trig ratios of given angles using a reference angle
    Define a periodic function
    Model periodic phenomena using periodic functions
    Define a quadrant angle

7. Work with Graphs of Periodic Functions

    Recognize and sketch graphs of sine and cosine functions and transformations of these functions of the form y = a sin (bx) + c and y = a cos (bx) + c
    Identify the period, amplitude and midline of a periodic function from its graph
    Identify the period, amplitude and midline of a periodic function from its equation

8. Work with Inverse Trigonometric Functions

    Define the inverse trigonometric functions of sine, cosine and tangent
    Evaluate, by hand, expressions involving inverse trig functions
    Evaluate, using technology, expressions involving inverse trig functions
    Describe the domain and ranges of inverse trigonometric functions
    Apply the inverse properties of trigonometric functions

9. Work with Trigonometric Identities and Relationships

    Use fundamental identities to simplify trigonometric expressions
    Verify trigonometric identities
    Factor trigonometric expressions
    Solve trigonometric equations using algebraic techniques
    Solve trigonometric equations using calculator
    Use the Law of Sine to solve oblique triangles
    Use the Law of Cosine to solve oblique triangles