MATH112

To develop an understanding of
a) trigonometry of angles,
b) trigonometry of triangles, and
c) trigonometry of functions.

To develop skills in
a) solving triangles,
b) proving trigonometric identities, and
c) solving trigonometric equations.

To develop familiarity with mathematical and physical applications of trigonometry.

To develop skills in the use of non-graphing scientific calculators with respect to trigonometric values.

Angles

1. Find the complement and the supplement of an angle.

2. Calculate and convert angle degrees, minutes, and seconds.

3. Find measures of co-terminal angles.

4. Use geometric properties which apply to angles.

5. Solve applied problems.

Basic Trigonometric Functions

1. Define the six trigonometric functions.

2. Define and use reciprocal identities.

3. Define and use Pythagorean identities.

4. Define and use quotient identities.

5. Identify signs, domains, and ranges for trigonometric functions.

Right Triangle Trigonometry

1. Define the six trigonometric functions based on right triangle trigonometry.

2. Write trigonometric functions in terms of cofunctions.

3. Find reference angles and use them to find exact trigonometric function values.

4. Find trigonometric function values using a non-graphing scientific calculator.

5. Solve applied problems using right triangles.

Unit Circle

1. Convert between degree and radian angle measures.

2. Find arc length and area of a sector for circles.

3. Draw and use the unit circle to find exact trigonometric function values.

4. Find linear and angular speed.

Graphs of the Trigonometric Functions

1. Graph sine and cosine functions.

2. Graph vertical and horizontal translations, expansions, and contractions for the sine and cosine functions.

3. Graph tangent and cotangent functions.

4. Graph secant and cosecant functions.

Trigonometric Identities

1. Verify trigonometric identities using fundamental identities.

2. Verify trigonometric identities using sum and difference identities.

3. Verify trigonometric identities using double- and half-angle identities.

Inverse Trigonometric Functions

a. Define inverse trigonometric functions for sine, cosine, and tangent.

b. Find inverse trigonometric function values for sine, cosine, and tangent.

c. Solve applied problems.

Trigonometric Equations

1. Solve trigonometric equations using algebraic and trigonometric methods.

2. Solve applied problems.

Oblique Triangle Trigonometry

1. Use the Law of Sines.

2. Use the Law of Cosines.

3. Solve applied problems.

Vectors

1. Interpret vectors algebraically.

2. Perform vector operations.

3. Solve applied problems.