MATH 1435 - Precalculus II: College Trigonometry

Credit Hours: 3.00

Objectives: The student will:

1. Draw angles in degrees and radians.
2. Convert angles between radians and degrees.
3. Find the arc length of a circle.
4. Find the area of a sector of a circle.
5. Find coterminal and reference angles.

Outcome 2: Upon completion of this course, students will be able to use and apply the trigonometry of right triangles.

Objectives: The student will:

1. Use the sine, cosine, tangent, cotangent, secant, and cosecant ratios to find exact values of trigonometric functions of acute angles.
2. Use the Reciprocal, Quotient, and Pythagorean Identities along with Complementary Angle Theorem to find exact trigonometric values of acute angles.
3. Solve right triangles and right triangle applications.
4. Find the exact values of the trigonometric functions of 30°-60°-90°.
5. Find the exact values of the trigonometric functions of 45°-45°-90°.

Outcome 3: Upon completion of this course, students will be able to evaluate and graph trigonometric functions.

Objectives: The student will:

1. Find the exact values of the six trigonometric functions of any angle using a point on the terminal side of the angle.
2. Determine the signs of the trigonometric functions of an angle in a given quadrant.
3. Use the reference angle to find the exact value of a trigonometric function.
4. Find the exact values of the six trigonometric functions of an angle using its corresponding point on the Unit Circle.
5. Know the domain and range of the six trigonometric functions.
6. Use coterminal angles, periodic properties, and even/odd properties to find exact values of the trigonometric functions.
7. Graph the six trigonometric functions f in the form y=Af(Bx-C)+D.
8. Find an equation of a trigonometric function from its graph.
9. Use the Law of Sines and Law of Cosines to solve non-right triangles and applications.
10. Find the area of a triangle.

Outcome 4: Upon completion of this course, students will be able to demonstrate knowledge of analytic trigonometry.

Objectives: The student will:

1. Know the domain and range of the six inverse trigonometric functions.
2. Find the exact values of inverse trigonometric functions.
3. Find the exact values of composite trigonometric functions involving inverses.
4. Solve trigonometric equations.
5. Establish trigonometric identities using fundamental identities and conjugates.
6. Use the sum, difference, double-angle, and half-angle formulas to find exact values and establish identities.

Outcome 5: Upon completion of this course, students will be able to demonstrate knowledge of and use the polar coordinate system.

Objectives: The student will:

1. Plot points using the polar coordinate system.
2. Convert between polar coordinates and rectangular coordinates.
3. Transform equations between polar and rectangular forms.
4. Graph polar equations by plotting points.

Outcome 6: Upon completion of this course, students will be able to demonstrate knowledge of and use vectors.

Objectives: The student will:

1. Graph vectors.
2. Find a position vector.
3. Add and subtract vectors geometrically and algebraically.
4. Find a scalar multiple of a vector.
5. Find the magnitude of a vector.
6. Find a unit vector.
7. Find the dot product of two vectors.

• Communication: The graduate can communicate effectively for the intended purpose and audience.
• Critical Thinking: The graduate can make informed decisions after analyzing information or evidence related to the issue.
• Global Literacy: The graduate can analyze human behavior or experiences through cultural, social, political, or economic perspectives.
• Information Literacy: The graduate can responsibly use information gathered from a variety of formats in order to complete a task.
• Quantitative Reasoning: The graduate can apply quantitative methods or evidence to solve problems or make judgments.
• Scientific Literacy: The graduate can produce or interpret scientific information presented in a variety of formats.

1. Trigonometric Functions
   1. Angles and their measure
      1. Draw angles in degrees and radians
      2. Convert from degrees to radians
      3. Convert from radians to degrees
      4. Find length of an arc of a circle
      5. Find area of a sector of a circle
      6. Coterminal and reference angles
   2. The Unit Circle
      1. Find the exact values of the six trigonometric functions using a point on the unit circle
      2. Find the exact values of the six trigonometric functions of quadrantal angles
   3. Properties of the trigonometric functions
      1. Find the domain and range of the six trigonometric functions
      2. Find the period of the six trigonometric functions
      3. Find the signs of the six trigonometric functions in a given quadrant
   4. Use transformations to graph y = Asin(Bx-C)+D, y = Acos(Bx-C)+D, y = Atan(Bx-C)+D, y = Acsc(Bx-C)+D, y = Asec(Bx-C)+D, and y= Acot(Bx-C)+D
2. Analytic Trigonometry
   1. Inverse trigonometric functions
      1. Find the domain and range of the 6 inverse trigonometric functions
      2. Find the exact value of all 6 inverse trigonometric functions
      3. Composite functions involving inverses
      4. Write a trigonometric expression as an algebraic expression in u
   2. Establish trigonometric identities
      1. Use fundamental identities
      2. Use a common denominator, factoring, conjugate, or any other algebraic technique
   3. Sum and difference formulas
      1. Find exact values
      2. Establish identities
      3. Find exact values involving inverse trigonometric functions
   4. Double and half-angle formulas
      1. Find exact values
      2. Establish identities
   5. Solving trigonometric equations
      1. Solve equations involving a single trigonometric function
      2. Solve equations involving multiple trigonometric functions
         1. Solve trigonometric equations in quadratic form
         2. Solve trigonometric equations using identities
3. Applications of Trigonometric Functions
   1. Right triangle trigonometric applications
      1. Find the value of trigonometric functions of acute angles
      2. Use the Complementary Angle Theorem
      3. Solve right triangles
      4. Solve applied problems including angles of elevation and depression
   2. Law of Sines
      1. Solve SAA or ASA Triangles
      2. Solve SSA Triangles
      3. Solve Applied Problems
   3. Law of Cosines
      1. Solve SAS Triangles
      2. Solve SSS Triangles
      3. Solve Applied Problems
   4. Area of a triangle
      1. Find the Area of SAS Triangles
      2. Find the Area of SSS Triangles using Heron’s Formula
4. Polar Coordinates
   1. Polar coordinates
      1. Plot points using polar coordinates
      2. Convert from polar coordinates to rectangular coordinates
      3. Convert from rectangular coordinates to polar coordinates
   2. Graph polar equations by plotting points
5. Vectors
   1. Graph Vectors
   2. Find a Position Vector
   3. Add and Subtract Vectors
   4. Find a Scalar Product of a Vector
   5. Find the Magnitude of a Vector
   6. Find a Unit Vector in the direction of the given vector
   7. Find the dot product of two vectors