Transcript title

Precalculus II: Trigonometry

Credits

4

Grading mode

Standard letter grades

Total contact hours

40

Lecture hours

40

Prerequisites

MTH 111Z or higher (except MTH 211, MTH 212, MTH 213, MTH 244, and STAT 243Z) or minimum placement Math Level 20.

Course Description

A course primarily designed for students preparing for calculus and related disciplines. This course explores trigonometric functions and their applications as well as the language and measurement of angles, triangles, circles, and vectors. These topics will be explored symbolically, numerically, and graphically in real-life applications and interpreted in context. This course emphasizes skill building, problem solving, modeling, reasoning, communication, connections with other disciplines, and the appropriate use of present-day technology.

Course learning outcomes

1. Translate among various systems of measure for angles including radians, degrees, and revolutions.
2. Represent, manipulate, and evaluate trigonometric expressions in terms of sides of a right triangle and in terms of the coordinates of a unit circle.
3. Graph, transform, and analyze trigonometric functions using amplitude, shifts, symmetry, and periodicity.
4. Manipulate trigonometric expressions and prove trigonometric identities.
5. Solve trigonometric equations using inverses, periodicity, and identities.
6. Define, represent, and operate with vectors both geometrically and algebraically.
7. Apply the law of sines and the law of cosines to determine lengths and angles.
8. Use variables, trigonometric functions, and vectors to represent quantities, create models, find solutions, and communicate an interpretation of the results.
9. Determine the reasonableness and implications of mathematical methods, solutions, and approximations in context.

Content outline

1. Angles
   1. Convert between angle measurements in degrees and radians.
   2. Identify the standard angles.
   3. Given an angle in degrees or radians, find one or more coterminal angles.
   4. Given a central angle of a circle, find the arc length that subtends it, or the area of the sector it encloses. Or, if you are given the arc length or sector area, find the angle.
   5. Find all six trig functions of any angle that either has its terminal side on an axis or has a reference angle of 30, 45, or 60 degrees.
   6. Find the reference angle for any angle in degrees or radians.
   7. Given two sides of a triangle and the angle between them, find the triangle’s area.
   8. Given one of the trig functions of an angle, as well as its quadrant (or enough information to figure out its quadrant), find the other five trig functions of the angle.
2. Triangles
   1. Given two pieces of information about a right triangle (side lengths and/or acute angle measures), solve the triangle.
   2. Solve application problems dealing with angles of depression or elevation using right triangle trigonometry.
   3. Use the Law of Sines to solve an ASA, SAA, or SSA triangle, possibly for an application.
   4. Identify whether an SSA triangle problem has 0, 1, or 2 solutions.
   5. Use the Law of Cosines to solve an SAS or SSS triangle, possibly for an application.
3. Trigonometric Graphs
   1. Know the domain and range of the inverse trig functions, and calculate either exact or approximate values of those functions.
   2. Identify the period, domain, and range of the functions y = sin x, y = cos x, and y = tan x.
   3. Identify the period, amplitude, and phase shift of a sine or cosine function, and graph one or two periods of the function. The 5 key points for each period should be clearly plotted.
   4. Find a possible sine or cosine equation for a given graph.
   5. Use a sine or cosine function to model sinusoidal behavior.
4. Algebra of Trig Functions
   1. Simplify trig expression or verify trig identities using the fundamental identities and algebra.
   2. Solve simple or factorable trig equations.
5. Vectors
   1. Define a vector using magnitude and direction.
   2. Represent a vector in various forms
   3. Apply vector operations of scalar multiplication, addition, and subtraction graphically and symbolically.
   4. Create unit vector in same direction as a given vector.
   5. Compute the dot product of two vectors.
      1. Understand the significance of the sign of the dot product as it applies to the orientation of the vectors.
      2. Find the angle between two vectors using the dot product.
6. Investigate at least two of the following applications.
   1. Tension in cables
   2. Work
   3. Component forces on objects
   4. Navigation
   5. Velocity vectors
   6. Other appropriate applied problems

Required materials

General education/Related instruction lists

• Science not Lab
• Mathematics