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Section 7.7

Section 7.7. Graphs of Tangent, Cotangent, Cosecant, and Secant Functions. GRAPHS OF TANGENT. Recall that the period of tangent is π . The graph of y = tan x has vertical asymptotes at. The period of y = tan ω x is π / ω . PROPERTIES OF THE TANGENT FUNCTION.

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Section 7.7

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  1. Section 7.7 Graphs of Tangent, Cotangent, Cosecant, and Secant Functions

  2. GRAPHS OF TANGENT Recall that the period of tangent is π. The graph of y = tan x has vertical asymptotes at The period of y = tan ωx is π/ω.

  3. PROPERTIES OF THE TANGENT FUNCTION • The domain is the set of all real numbers, except odd multiples of π/2. • The range consists of all real numbers. • The tangent function is an odd function, as the symmetry of the graph with respect to the origin indicates. • The tangent function is periodic, with period π. • The x-intercepts are . . . , −2π, −π, 0, π, 2π, . . . ; the y-intercept is 0. • Vertical asymptotes occurs at x = . . . , −3π/2, −π/2, π/2, 3π/2, . . . .

  4. GRAPHS OF COTANGENT Recall that the period of cotangent is π. The graph of y = cot x has vertical asymptotes at x = 0, ±π, ±2π, ±3π, … . The period of y = cot bx is π/b.

  5. GRAPHS OF SECANT Recall that the period of secant is 2π. The graph of y = sec x has vertical asymptotes at The period of y = sec bx is 2π/b.

  6. GRAPHS OF COSECANT Recall that the period of cosecant is 2π. The graph of y = csc x has vertical asymptotes at x = 0, ±π, ±2π, ±3π, … . The period of y = csc bx is 2π/b.

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