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Unformatted text preview: Section 4.4 – Trigonometric Expressions and Identities 1 Section 4.4 Trigonometric Expressions and Identities In this section we are going to practice the algebra involved in working with the trigonometric functions. This will help to pave the way for the more analytical parts of trigonometry in the next chapter. An identity is an equation that is satisfied by all relevant values of the variables concerned. An example of an identity is 2 2 ) )( ( y x y x y x- = +- . In simplifying identities it may be useful to use the following. Basic Trigonometric Identities 1. 1 cos sin 2 2 = + θ θ 2. θ θ θ tan cos sin = 3. θ θ cos 1 sec = ; θ θ sin 1 csc = ; θ θ tan 1 cot = (Reciprocal Identities) 4. Pythagorean Identities: 1 ) ( cos ) ( sin 2 2 = + θ θ ) ( sec 1 ) ( tan 2 2 θ θ = + ) ( csc 1 ) ( cot 2 2 θ θ = + Notational Conventions 1. An expression such as sin θ really means sin( θ ), where sin or sine is the name of the function and θ is an input. An exception to this, however, occurs in expressions such as...
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