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 DISTRICT CAMPUS

## Trigonometry Syllabus

Trigonometry

Course Description: Trigonometry is the study of the solution of all triangles using ratios and angles.  Trig can be used to solve problems related to astronomy, surveying, and construction, to name only a few areas.

Resources: Trigonometry Text (Addison -Wesley 7th edition)

I.  First Nine Weeks

1. The Trigonometric Functions
1. Review of coordinate plane, Pythagorean Theorem, Distance Formula, interval notation, relations and functions, and function notation.
2. Review of angles
3. Converting between decimal degrees and degrees, minutes, and seconds
4. Find the measures of coterminal angles.
5. Review of angles formed by two lines cut by a transversal.
6. Be able to find missing angles in a triangle and in similar triangles.
7. Be able to classify triangles.
8. Know and use the 6 trig functions.
9. Find the function values of an angle.
10. Find the function values of quadrantal angles.
11. Learn and use the reciprocal identities.
12. Memorize the Pythagorean identities and the Quotient Identities.
13. Find function values given one value and the quadrant

1. Acute Angles and Right Angles
1. Learn the cofunction identities and write functions in terms of cofunctions.
2. Solve equations using the cofunction identities.
3. Be able to use the trig function values of special angles.
4. Define reference angles and find their values.
5. Find trig function vales for any nonquadrantal angle using reference angles.
6. Find angle measures given an interval and a function value.
7. Find trig functions values using a calculator.
8. Perform calculations using significant digits.
9. Solve triangles using trig ratios and significant digits.

1. Radian Measure and the Circular Functions
1. Be able to convert degrees to radians and radians to degrees.
2. Find function values of an angle in radian measure.
3. Find arc lengths of circles.
4. Find values of circular functions.
5. Determine a number with a given circular function value.
6. Apply circular functions.
7. Find angular velocity and linear velocity.

1. Graphs of Circular Functions
1. Use periodic functions to solve problems.
2. Understand the graph of the sine function and the graph of the cosine function.
3. Understand amplitude and periods of sine and cosine graphs.
4. Graph using horizontal translations, vertical translations, and combinations of translations.
5. Determine a trig model using curve fitting.
6. Understand graphs of cosecant and secant functions.
7. Understand graphs of tangent and cotangent functions.
8. Graph using addition of ordinates.

II. Second Nine Weeks

1. Trigonometric Identities
1. Review the basic identities- reciprocal, quotient, and Pythagorean.
2. Use negative-angle identities to solve.
3. Express one function in terms of another.
4. Verify identities by working with one side.
5. Verify identities by  working with both sides.
6. Use the cosine sum and difference identities to find exact values.
7. Use cofunction identities to find an angle measure.
8. Apply the sum and difference identities.
9. Verify Identities with double angles.
10. Apply double-angle identities.
11. Apply half-angle identities.

1. Inverse Trigonometric Functions and Trigonometric Equations
1. Review inverse function concepts.
2. Find inverse values.
3. Find function values using inverse function values.
4. Solve trig equations using linear methods, factoring, quadratic formula or graphing.
5. Solve inverse trigonometric equations.

1. Applications of Trig and Vectors
1. Solve oblique triangles using congruence axioms.
2. Use Law of Sines to solve a triangle.
3. Use Law of SInes in an application.
4. Find the area of a triangle using Law of SInes.
5. Look at the ambiguous case of Law of Sines.
6. Solve SSA triangles.
7. Use Law of Cosines to solve a triangle.
8. Use Law of Cosines in an application.
9. Solve SAS and SSS triangles.
10. Use Heron’s Formula to find the area of a triangle.
11. Find magnitudes of vertical and horizontal components of vectors.
12. Find the magnitude of the resultant of two vectors in applications.
13. Perform vector operations.
14. Find the dot product.