Trigonometry is a branch of mathematics that deals with relationships between the sides and the angles of a triangle and with the trigonometric functions, which describe those relationships.
Trigonometry videos include the following topics:
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We begin this subject by refreshing our skills from Algebra inlcuding operations with Real numbers; solving equations and inequalities; as well as graphing lines and functions in the Rectangular Coordinate system.
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In this topic, we explore much of the fundamental relationships in trigonometry. We explore the concepts of angles in degrees, radians, degrees minutes seconds, and co-terminal angles; the relationships between the trigonometric functions sine, cosine, tangent, secant, cosecant, and cotangent in a right triangle, from the unit circle, and with identities. Next, we exploring graphing trigonometric functions including basic graphs, periods, amplitudes, vertical shifts and phase shifts. We completely explore finding values from the unit circle for the 6 trigonometric functions in radians and degrees by drawing angles and reference angles. We finish by exploreing solving right triangles and their applications to real world scenarios.
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At this point, we turn our attention to various formulas and identities between the 6 trigonometric functions. We start by completely exploring many problems involving identities. Next, we explore trigonometric formulas such as the sum and difference formulas; double angle and half angle formulas and the product-to-sum and sum-to product formulas and their applications.
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This topic explores further applications of Trigonometry such as The Law of Sines (and it's ambiguous case), the Law of Cosines; the Trigonometric Form of complex numbers as well as Demoivre's Theorem to find powers and roots of complex numbers. We finish this topic by exploring vectors, how to sketch vectors in a plane, arithmetic operations of vectors and the dot product between two vectors.
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We conclude Trigonometry with the further exploration of Exponential and Logarithmic Functions. Topics include graphing exponential and logarithmic functions, solving exponential and logarithmic equations, using properties of logarithms including writing expressions in exponential or logarithmic form and using logarithms to solve real world applications.
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