This course begins by covering basic fundamentals of trigonometry. It accelerates quickly into more advanced trigonometry applications that encompass principles of science, technology, and engineering. Lessons will provide step-by-step guidance through procedures and solutions, providing clear examples for each type of problem. Students will explore concepts from radian and degree measurement to unit circles, trigonometric functions, and sine and cosine functions. This course is geared for students in grades 11-12 with an interest in pursuing engineering-related coursework.
It is recommended that students successfully complete Algebra II or equivalent course work and have a solid understanding of Algebra II concepts before enrolling in this course.
Unit 1: Essential Content and Skills
- Analyze, plot, and convert angles measured in degrees and radians.
- Calculate linear speed and angular speed of a rotating circular object.
- Find the values of the trigonometric functions of common angles given in degrees and in radians.
- Solve right triangles with one given side and one given angle.
- Determine domain and range of a function given as a graph, equation, table, or verbal statement.
- Determine whether a function given as a graph or an equation is odd, even, or neither.
- Chart functions using transformations.
- Use period and symmetry to evaluate trigonometric functions of given angles.
Unit 2: Essential Content and Skills
- Chart basic sine and cosine functions.
- Determine the amplitude, period, phase shift, vertical and horizontal translations, and possible asymptotes of a trigonometric function from the graph and equation.
- Recognize and write the fundamental trigonometric identities.
- Use sum and difference identities to evaluate and verify trigonometric functions.
- Use double angle formulas to simplify and evaluate trigonometric expressions.
- Simplify and verify trigonometric identities containing multiple angle trigonometric expressions.
Unit 3: Essential Content and Skills
- Use product-to-sum and sum-to product formulas to evaluate trigonometric functions and verify trigonometric identities.
- Write a given function as a composition of two functions.
- Chart inverse trigonometric functions: arcsine, arccosine, and arctangent.
- Evaluate inverse trigonometric functions and compositions thereof.
- Solve problems involving right triangles.
- Write equations and identify amplitude, frequency, and period in an equation of simple harmonic motion.
- Use inverse trigonometric functions and algebraic methods to solve trigonometric equations.
Unit 4: Essential Content and Skills
- Solve oblique triangles by using the Law of Sines and the Law of Cosines.
- Find the area of an oblique triangle using the area formula and Heron's Area Formula.
- Develop an understanding of vector operations, unit vectors, and the dot product.
- Apply trigonometry in various careers in the real world.
*Available as an iText course