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Sine Function : f(x) = sin (x)Domain: Range: Period = x intercepts: x = ________ , where k is an integery intercepts: Maxima: (________,_____) where k is an integerMinima: (________,_____) where k is an integerSymmetry: Intervals of increase/decrease (from 0 to 2π): sin (x) is increasing on the intervals _________ and __________ and decreasing on the interval ____________Cosecant Function : f(x) = csc (x)Domain: all real numbers except k pi, k is an integer. Range: (- , -1] U [1 , +) Period = 2pi x intercepts:y intercepts:symmetry: intervals of increase/decrease (from 0 to 2 π): decreasing on (_______) U (_________) and increasing on (_______) U (_________) Vertical asymptotes: x = ________, where k is an integerCosine Function : f(x) = cos (x)Domain: Range: Period = x intercepts: x = ________ , where k is an integer y intercepts: Maxima: (________,_____) where k is an integerMinima: (________,_____) where k is an integersymmetry: intervals of increase/decrease (from 0 to 2 π): cos (x) is decreasing on ________ and increasing on _________ Secant Function : f(x) = sec (x)Domain: Range: Period = x intercepts:y intercepts: symmetry: intervals of increase/decrease (from 0 to 2π): increasing on (________) U (_______) and decreasing on (________) U (_________). Vertical asymptotes: x = ________, where k is an integer.Tangent Function : f(x) = tan (x)Domain: Range: Period = x intercepts: x = ______ where k is an integer. y intercepts: y = Symmetry: Intervals of increase/decrease:Vertical asymptotes: x = __________, where k is an integer. Cotangent Function : f(x) = cot (x)Domain: Range: Period = x intercepts: x = __________, where k is an integer. y intercepts:symmetry: intervals of increase/decrease: Vertical asymptotes: x = __________ where k is an integer. Answer key:Sine Function : f(x) = sin (x)Graph SINEDomain: all real numbers Range: [-1 , 1] Period = 2pi x intercepts: x = k pi , where k is an integer. y intercepts: y = 0 maximum points: (pi/2 + 2 k pi , 1) , where k is an integer. minimum points: (3pi/2 + 2 k pi , -1) , where k is an integer. symmetry: since sin(-x) = - sin (x) then sin (x) is an odd function and its graph is symmetric with respect to the origon (0 , 0). intervals of increase/decrease: over one period and from 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and (3pi/2 , 2pi), and decreasing on the interval (pi/2 , 3pi/2). Cosine Function : f(x) = cos (x)Graph COSINEDomain: all real numbers Range: [-1 , 1] Period = 2pi x intercepts: x = pi/2 + k pi , where k is an integer. y intercepts: y = 1 maximum points: (2 k pi , 1) , where k is an integer. minimum points: (pi + 2 k pi , -1) , where k is an integer. symmetry: since cos(-x) = cos (x) then cos (x) is an even function and its graph is symmetric with respect to the y axis. intervals of increase/decrease: over one period and from 0 to 2pi, cos (x) is decreasing on (0 , pi) increasing on (pi , 2pi). Tangent Function : f(x) = tan (x)Graph TANGENTDomain: all real numbers except pi/2 + k pi, k is an integer. Range: all real numbers Period = pi x intercepts: x = k pi , where k is an integer. y intercepts: y = 0 symmetry: since tan(-x) = - tan(x) then tan (x) is an odd function and its graph is symmetric with respect the origin. intervals of increase/decrease: over one period and from -pi/2 to pi/2, tan (x) is increasing. Vertical asymptotes: x = pi/2 + k pi, where k is an integer. Cotangent Function : f(x) = cot (x)Graph Domain: all real numbers except k pi, k is an integer. Range: all real numbers Period = pi x intercepts: x = pi /2 + k pi , where k is an integer. symmetry: since cot(-x) = - cot(x) then cot (x) is an odd function and its graph is symmetric with respect the origin. intervals of increase/decrease: over one period and from 0 to pi, cot (x) is decreasing. Vertical asymptotes: x = k pi, where k is an integer. Secant Function : f(x) = sec (x)Graph SECANTDomain: all real numbers except pi/2 + k pi, n is an integer. Range: (-infinity , -1] U [1 , +infinity) Period = 2 pi y intercepts: y = 1 symmetry: since sec(-x) = sec (x) then sec (x) is an even function and its graph is symmetric with respect to the y axis. intervals of increase/decrease: over one period and from 0 to 2 pi, sec (x) is increasing on (0 , pi/2) U (pi/2 , pi) and decreasing on (pi , 3pi/2) U (3pi/2 , 2pi). Vertical asymptotes: x = pi/2 + k pi, where k is an integer. Cosecant Function : f(x) = csc (x)Graph COSECANTDomain: all real numbers except k pi, k is an integer. Range: (-infinity , -1] U [1 , +infinity) Period = 2pi symmetry: since csc(-x) = - csc(x) then csc (x) is an odd function and its graph is symmetric with respect the origin. intervals of increase/decrease: over one period and from 0 to 2pi, csc (x) is decreasing on (0 , pi/2) U (3pi/2 , 2pi) and increasing on (pi/2 , pi) U (pi / 3pi/2). Vertical asymptotes: x = k pi, where k is an integer. ................
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