The properties of the 6 trigonometric functions: sin (x), cos (x), tan(x), cot (x), sec (x) and also csc (x) space discussed. These incorporate the graph, domain, range, asymptotes (if any), symmetry, x and y intercepts and maximum and minimum points.

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Sine duty : f(x) = sin (x)

Domain: all actual numbersRange: <-1 , 1>Period = 2pix intercepts: x = k pi , wherein k is one integer.y intercepts: y = 0maximum points: (pi/2 + 2 k pi , 1) , where k is one integer.minimum points: (3pi/2 + 2 k pi , -1) , where k is one integer.symmetry: since sin(-x) = - sin (x) climate sin (x) is one odd role and that is graph is symmetric v respect to the origin (0 , 0).intervals the increase/decrease: end one duration and indigenous 0 to 2pi, sin (x) is increasing on the intervals (0 , pi/2) and also (3pi/2 , 2pi), and also decreasing on the term (pi/2 , 3pi/2).

Cosine function : f(x) = cos (x)

Domain: all actual numbersRange: <-1 , 1>Period = 2pix intercepts: x = pi/2 + k pi , where k is an integer.y intercepts: y = 1maximum points: (2 k pi , 1) , wherein k is an integer.minimum points: (pi + 2 k pi , -1) , wherein k is an integer.symmetry: because cos(-x) = cos (x) climate cos (x) is an even role and that graph is symmetric with respect come the y axis.intervals of increase/decrease: over one duration and native 0 come 2pi, cos (x) is to decrease on (0 , pi) raising on (pi , 2pi).

Tangent duty : f(x) = tan (x)

Domain: all real numbers other than pi/2 + k pi, k is one integer.Range: all genuine numbersPeriod = pix intercepts: x = k pi , whereby k is one integer.y intercepts: y = 0symmetry: due to the fact that tan(-x) = - tan(x) climate tan (x) is an odd role and the graph is symmetric v respect the origin.intervals the increase/decrease: end one duration and from -pi/2 to pi/2, tan (x) is increasing.Vertical asymptotes: x = pi/2 + k pi, wherein k is an integer.

Cotangent duty : f(x) = cot (x)

Domain: all actual numbers except k pi, k is an integer.Range: all actual numbersPeriod = pix intercepts: x = pi /2 + k pi , whereby k is one integer.symmetry: because cot(-x) = - cot(x) then cot (x) is an odd function and that is graph is symmetric v respect the origin.intervals that increase/decrease: over one duration and from 0 come pi, cot (x) is decreasing.Vertical asymptotes: x = k pi, whereby k is one integer.

Secant duty : f(x) = sec (x)


Domain: all actual numbers except pi/2 + k pi, n is an integer.Range: (-infinity , -1> U <1 , +infinity)Period = 2 piy intercepts: y = 1symmetry: due to the fact that sec(-x) = sec (x) then sec (x) is an even duty and that is graph is symmetric through respect come the y axis.intervals that increase/decrease: end one duration and native 0 come 2 pi, sec (x) is increasing on (0 , pi/2) U (pi/2 , pi) and also decreasing ~ above (pi , 3pi/2) U (3pi/2 , 2pi).Vertical asymptotes: x = pi/2 + k pi, whereby k is an integer.

Cosecant duty : f(x) = csc (x)

Domain: all actual numbers other than k pi, k is an integer.Range: (-infinity , -1> U <1 , +infinity)Period = 2pisymmetry: due to the fact that csc(-x) = - csc(x) then csc (x) is one odd role and its graph is symmetric through respect the origin.intervals the increase/decrease: end one duration and native 0 to 2pi, csc (x) is decreasing on (0 , pi/2) U (3pi/2 , 2pi) and increasing top top (pi/2 , pi) U (pi / , 3pi/2).

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Vertical asymptotes: x = k pi, wherein k is an integer.