sin(-0) = = - sin 0 cos(-0). = cos 0 tan(-0). = - tan 0. 1. 1. 1 sin 0 = cos. = tan 0 = CSC 0 sec @ cot @. 1. 1. 1 csc(-0). = - csc 0 sec(-0) = sec✪ cot(-0). |
Periodicity. Cofunction sin (x + 2 ) = sinx cos (x + 2 ) = cosx csc (x + 2 ) = cscx sec (x + 2 ) = secx tan (x + ) = tanx cot (x + ) = cotx sinx = cos. |
The eight basic trigonometric identities are listed in Table 1. As we will see, they are all derived from the definition of the trigonometric functions. |
Example 1: Replace a. tan cos 0. Use Trigonometric Identities to write each expression in terms of a single trigonometric identity or a constant. |
We are going to use these to help us solve particular kinds of trigonometrical equations. Example. Suppose we wish to solve the equation. 2 tan2 x = sec2 x for ... |
Usually the best way to begin is to express everything in terms of sin and cos. Examples. 1. Simplify the function cosxtanx. cosxtanx = cosx × sinx cosx. = sinx. |
Even/Odd Formulas sin(−θ) = −sin(θ) csc(−θ) = −csc(θ) cos(−θ) = cos(θ) sec(−θ) = sec(θ) tan(−θ) = −tan(θ) cot(−θ) = −cot(θ). Periodic Formulas. |
For example, x2 y2 (x y)(x y) is an algebraic identity. An identity involving trigonometric expressions is called a trigonometric identity. If you can show that ... |
8. tan2 x sin' x = tan' x - sin' x. Page 2. Tria. Prove each identity: 1. 3. 5. 7. . 1 secx-tonxslnx= - - sec X seellsinll tane + cote sin'lI. , ., 12·'. |
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