PP Section 7.5

PP Section 7.5 - entire basic graph of tangent will take...

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Graph of Tangent and the Reciprocal Functions

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y = tan(x) tan sin cos x x x = The tangent function is undefined when cos(x) = 0. odd , 2 OR 2 2 0 ) cos( 2 3 2 n n x n n x x π = + + = = The graph of the tangent function has vertical asymptotes at all the above x values.
The Graph of y = tan x x y - - - π 3 4 6 0 6 4 3 3 1 58 . 0 3 3 0 58 . 0 3 3 1 73 . 1 3 - - - - -

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y = tan(x)
Characteristics of the Tangent Function 2. The range consists of all real numbers, so NO amplitude. . 3. The tangent function is an odd function (symmetric with respect to the origin). 4. The tangent function is periodic, with period . π 0). (0, is intercept - the , 2 , 0, , - , ,-2 at are intercepts - The . 5 y x 1. The domain is the set of all real numbers except odd multiples of π/2, where there are asymptotes.

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) 2 tan( of graph Sketch the x y = 4 4 2 2 2 π < < - < < - x x This means that the period has been changed. The

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Unformatted text preview: entire basic graph of tangent will take place over the new interval. The asymptotes of the graph will be at the end of the new interval and spaced π/2 units apart. y = tan(2x) Graphs of the Reciprocal Functions The graphs of cotangent, secant, and cosecant can be sketched using the fact that they are the reciprocals of tangent, cosine, and sine, respectively. Start by graphing the appropriate function, and then take the reciprocal. Asymptotes are drawn at the x-intercepts of the original function. Sine and Cosecant y = sin(x) y = csc(x) Cosine and Secant y = cos(x) y = sec(x) Tangent and Cotangent y = tan(x) y = cot(x)...
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This note was uploaded on 01/22/2011 for the course MATH 2 taught by Professor Gardner during the Fall '08 term at Irvine Valley College.

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PP Section 7.5 - entire basic graph of tangent will take...

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