Grade: 11-12
Credit: one-half
Prerequisite: Algebra 2

Trigonometry topics include circular functions, right triangle ratios, solutions of trigonometric equations, inverses, identities, the laws of sines and cosines, graphs of trigonometric functions, and applications of trigonometric techniques to solve real-world problems. A transformational approach to graphing is used with families of related graphs. Numerical, graphical, and algebraic solutions should be considered for all problems where appropriate. Graphing utilities, especially graphing calculators, are integral to the course.

Indicators marked with an asterisk * relate directly to the Virginia Standards of Learning for Trigonometry. All Virginia Standards of Learning for Trigonometry are included in this course.

Benchmarks and indicators are organized by the following strands:

1. Review of Algebraic Fundamentals
2. Mechanics
3. Solving Triangles
4. Identities
5. Graphs
6. Vectors and Polars

Benchmark
Students analyze, describe, and compare a variety of functions and relations.

1. Determine whether a given relation is a function and identify the domain and range.
2. Perform operations with functions, find composite functions, and find the inverse of a given function, if it exists.
3. Use transformations to graph simple functions (e.g., y = Af(Bx + C) + D)

Benchmark
Students apply algebraic techniques to analyze, describe, and compare trigonometric equations and functions.

1. Change from radian to degree measure and vice versa, find angles that are coterminal with a given angle, and find the reference angle for a given angle.
2. Find the exact and approximate values of the six trigonometric functions of an angle in standard position. Circular functions, the unit circle, and the right triangle will be interrelated.*
3. Find exact and approximate answers for the six trigonometric functions of special angles.*
4. Evaluate inverse trigonometric relations and functions.*
5. Solve trigonometric equations graphically and algebraically.*
6. (optional) Find the length of an arc, linear speed, and angular velocities.

Benchmark
Students solve real-world problems conducive to right triangle solutions.

1. Solve right triangles and apply solutions to real-world problems.*
2. Apply the law of sines and the law of cosines to the solution of real-world problems involving triangles.*
3. Find the area of triangles using Hero's formula and the sine formula.

Benchmark
Students apply algebraic techniques to establish and verify trigonometric relationships.

1. Identify and use reciprocal identities, quotient identities, and Pythagorean identities to simplify expressions, verify other identities, and solve equations.*
2. Use the sum and difference identities and double angle identities to verify other trigonometric identities and solve equations.*
3. (optional) Use the half-angle identities to verify other trigonometric identities and solve equations.

Benchmark
Students apply a transformational approach with graphing calculators to analyze, describe, and compare a variety of trigonometric functions.

1. Find the domain, range, amplitude, period, phase shift, and vertical displacement and sketch the graph of each of the six trigonometric functions given an equation in standard form (e.g., y = Asin(Bx + C) + D) by using transformations for at least one period.*
2. Write equations of trigonometric functions given the amplitude, period, phase shift, and vertical displacement.
3. *Graph inverse trigonometric functions and identify their domain and range.
4. (optional) Graph compound trigonometric functions using addition of ordinates.

Students will analyze, describe, compare, and apply multiple representations to a variety of graphs.

1. Find equal, opposite, and parallel vectors and add and subtract them geometrically.
2. Find ordered pairs that represent vectors and add, subtract, multiply, and find the magnitude of vectors algebraically.
3. Solve real-world problems using vectors.*
4. (optional) Investigate and identify the characteristics of the graphs of polar equations using a graphing calculator. Change points and equations from polar to rectangular form and vice versa, classify polar equations, predict the effects of changes in the constants, and find points of intersections of polar graphs.

Assessment
There is no Virginia Standards of Learning Test for Trigonometry.

Last update: August 21, 1998