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Trigonometry
In this course, students learn the basic concepts of Trigonometry and application of these concepts to problem solving.
The stress of this course is done on three key elements of Trigonometry:
1. Trigonometric functions and their inverses.
2. Trigonometric transformations.
3. Trigonometric identities, equations and inequalities.
Concepts introduction and problem solving form an integral part of each class session. Students learn extensively from and by examples, and a variety of instructional methods are used to enhance students' problem-solving abilities. Students tackle many complicated problems using inductive and deductive reasoning approaches. Some of the topics and problems that are studied in this course include:
Right triangle trigonometry.
Trigonometric ratios of special angles.
Solving right triangles.
Trigonometric functions of general angles.
Radian and degree measure of angles. Conversion between degrees and radians.
Arc length. Angular and linear speed.
Wrapping functions. Circular functions.
Fundamental trigonometric identities:
Quotient identities
Reciprocal identities
Pythagorean identities
Cofunction identities
Reduction identities
Symmetric identities
General strategies for verifying trigonometric identities.
Elementary graphs of trigonometric functions. Domain. Range. Amplitude. Period.
Trigonometric graph transformations. Phase shift. Vertical shift.
Damped trigonometric functions.
Sum and difference formulas.
Multiple and half angle formulas.
Product-to-sum and sum-to-product formulas.
Inverse trigonometric functions, their graphs and compositions.
Elementary Trigonometric equations.
Different types of trigonometric equations including quadratic and homogeneous.
Elementary trigonometric inequalities and their graphs.
Multiple steps trigonometric inequalities.
Simple harmonic motion.
“Law of Sines”. “Law of Cosines”. “Law of Tangents”.
Solving scalene triangles.
Area of triangle. Heron’s area formula. Area of a convex quadrilateral.
Trigonometric form of complex numbers.
Multiplication and division of complex numbers in trigonometric form.
Powers and roots of complex numbers in trigonometric form. De Moivre Theorem.
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