Graphs of Tangent Cotangent I Graph of the

Graphs of Tangent & Cotangent I. Graph of the Tangent function. A) tanθ = y/x. (use the Unit Circle to get points) θ x y tan θ 0 1 0 0 ½ . 58 30 45 1 60 ½ 90 0 1. 7 1 undef

Graphs of Tangent & Cotangent I. Graph of the Tangent function. B) Graph is

Graphs of Tangent & Cotangent II. Graph of the Cotangent function. A) Since cot is the reciprocal of tangent and tan = then cot = B) Graph of cot is…

Graphs of Tangent & Cotangent III. Period, Domain / Range & Asymptotes of tan & cot. A) Period = π B) Domain (the x values). All values except… 1) tan: x ≠ π/2, 3π/2, 5π/2, etc. (or -π/2, -3π/2, etc. ) 2) cot: x ≠ 0, π, 2π, 3π, etc. (or –π, -2π, etc. ) C) Range: (the y values) both are all real numbers. 1) (-∞, +∞) or Range = {R} D) Vertical asymptotes (lines graphs never cross). 1) tan: x = π/2 + nπ 2) cot: x = nπ (x = π/2, x = 3π/2, x = 5π/2, etc) (x = 0, x = π, x = 2π, etc. )

Graphs of Tangent & Cotangent IV. Transformations of Tangent & Cotangent functions. Standard form: y = D + A trig B(x + C) A) Vertical asymptote shift: 1) set Bx = “the normal vertical asymptotes”. Solve for x, this is the period shifted asymptotes. a) tan: Bx = -π/2 and Bx = π/2 b) cot: Bx = 0 and Bx = π B) Horizontal & Vertical shifts (same as other trig). 1) Change the sign of the C. This is the sideways shift. 2) The “D” is the vertical shift (move the graph up/down).