Trigonometric Identities HRSBSTAFF Home Page(三角恒等式HRSBSTAFF主页).doc
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Throughout this section you will learn basic Trigonometric Identities: Reciprocal Identities, Pythagorean Identities and Quotient Identities. By learning the three above noted identities, you will then learn how to Prove Identities. Every topic links together to make it more comprehensible. Trigonometric Identities are just a section of Trigonometry. The Law of Cosines, the Law of Sines, the Pythagorean Theorem and Right Angle Triangles each play a
part in learning identities.
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TRIGONOMETRY
Discovered in the 17th century and is derived from the Latin word trigonometria. This is defined as the study of the Triangle and of the relationships between the angles and sides of a triangle, plus the deduction of certain components of the triangle when others are known.
TRIGONOMETRIC IDENTITES
This comes from the basics of trigonometry, dealing with the relations of the sides and angles of triangles. Each trigonometric identity has a reciprocal identity.
IDENTITIES
Discovered in the 16th century and comes from the Latin word Identitas, which are equations that are true for all values of the variable for which they are defined.
Now that we know the definition for “Trigonometr(y)/ (ic) Identities”, we can move onto trigonometric functions. For most trigonometric functions the three functions, Sine, Cosine and Tangent are used most frequently. Throughout this unit of Trigonometric Identities, three more functions are added, Cotangent, Secant and Cosecant. There are six ways of making ratios of two sides of a right angle. So, remember each identity has a reciprocal identity. As long as you can remember that, then learning the identities will not be difficult.
a chart of the six functions and their values.
Identity Letter from Triangle Position on Triangle SinA= a/c Opposite/ Hypotenuse CosA= b/c Adjacent/ Hypotenuse TanA= a/b Opposite/ Adjacent CotA= b/a Adjacent/ Opposite SecA= c/b Hypotenuse/ Adjacent CscA= c/a Hypot
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