`color(red)(star)` Sine Function : `f(x) = sin (x)`

`color(red)(star)` Cosine Function :` f(x) = cos (x)`

`color(red)(star)` Tangent Function `: f(x) = tan (x) `

`color(red)(star)` Cotangent Function `: f(x) = cot (x) `

`color(red)(star)` Secant Function `: f(x) = sec (x)`

`color(red)(star)` Cosecant Function `: f(x) = cosec (x)`

`color(red)(star)` Cosine Function :` f(x) = cos (x)`

`color(red)(star)` Tangent Function `: f(x) = tan (x) `

`color(red)(star)` Cotangent Function `: f(x) = cot (x) `

`color(red)(star)` Secant Function `: f(x) = sec (x)`

`color(red)(star)` Cosecant Function `: f(x) = cosec (x)`

`color(red)(✍️ ul "Domain :")` all real numbers

`color(green)(✍️ ul "Range :")` `" "[-1 , 1]`

`color(red)(✍️ ul "Period = ")` `2pi`

`color(green)(✍️ ul "x intercepts : ")` `color(blue)(x = k pi)` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `color(blue)(y = 0)`

`color(green)(✍️ ul "maximum points :")` `color(blue)((pi/2 + 2 k pi "," 1))` , where `k` is an integer.

`color(red)(✍️ ul "Minimum points :")` `color(blue)(((3pi)/2 + 2 k pi "," -1))` , where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `color(blue)(sin(-x) = - sin (x))` then `sin (x)` is an odd function and its graph is symmetric with respect to the origin `(0 , 0).`

`color(red)(✍️ ul "Iintervals 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).`

`color(green)(✍️ ul "Range :")` `" "[-1 , 1]`

`color(red)(✍️ ul "Period = ")` `2pi`

`color(green)(✍️ ul "x intercepts : ")` `color(blue)(x = k pi)` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `color(blue)(y = 0)`

`color(green)(✍️ ul "maximum points :")` `color(blue)((pi/2 + 2 k pi "," 1))` , where `k` is an integer.

`color(red)(✍️ ul "Minimum points :")` `color(blue)(((3pi)/2 + 2 k pi "," -1))` , where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `color(blue)(sin(-x) = - sin (x))` then `sin (x)` is an odd function and its graph is symmetric with respect to the origin `(0 , 0).`

`color(red)(✍️ ul "Iintervals 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).`

`color(red)(✍️ ul "Domain :")` all real numbers

`color(green)(✍️ ul "Range :")` ` [-1 , 1]`

`color(red)(✍️ ul "Period = ")` ` 2pi`

`color(green)(✍️ ul "x intercepts : ")` `x = pi/2 + k pi` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `y = 1`

`color(green)(✍️ ul "maximum points :")` `(2 k pi , 1)` , where `k` is an integer.

`color(red)(✍️ ul "Minimum points :")` ` (pi + 2 k pi , -1) `, where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `cos(-x) = cos (x)` then `cos (x)` is an even function and its graph is symmetric with respect to the y axis.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `0` to `2pi, cos (x)` is decreasing on `(0 , pi)` increasing on `(pi , 2pi)`.

`color(green)(✍️ ul "Range :")` ` [-1 , 1]`

`color(red)(✍️ ul "Period = ")` ` 2pi`

`color(green)(✍️ ul "x intercepts : ")` `x = pi/2 + k pi` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `y = 1`

`color(green)(✍️ ul "maximum points :")` `(2 k pi , 1)` , where `k` is an integer.

`color(red)(✍️ ul "Minimum points :")` ` (pi + 2 k pi , -1) `, where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `cos(-x) = cos (x)` then `cos (x)` is an even function and its graph is symmetric with respect to the y axis.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `0` to `2pi, cos (x)` is decreasing on `(0 , pi)` increasing on `(pi , 2pi)`.

`color(red)(✍️ ul "Domain :")` all real numbers except `pi/2 + k pi, k` is an integer.

`color(green)(✍️ ul "Range :")` all real numbers

`color(red)(✍️ ul "Period = ")` ` pi`

`color(green)(✍️ ul "x intercepts : ")` `x = k pi` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `y = 0`

`color(green)(✍️ ul "Symmetry:")` since `tan(-x) = - tan(x)` then `tan (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `-pi/2` to `pi/2, tan (x)` is increasing.

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = pi/2 + k pi`, where `k` is an integer.

`color(green)(✍️ ul "Range :")` all real numbers

`color(red)(✍️ ul "Period = ")` ` pi`

`color(green)(✍️ ul "x intercepts : ")` `x = k pi` , where `k` is an integer.

`color(red)(✍️ ul "y intercepts : ")` `y = 0`

`color(green)(✍️ ul "Symmetry:")` since `tan(-x) = - tan(x)` then `tan (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `-pi/2` to `pi/2, tan (x)` is increasing.

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = pi/2 + k pi`, where `k` is an integer.

`color(red)(✍️ ul "Domain :")` all real numbers except `k pi, k` is an integer.

`color(green)(✍️ ul "Range :")` all real numbers

`color(red)(✍️ ul "Period = ")` ` pi`

`color(green)(✍️ ul "x intercepts : ")` ` x = pi /2 + k pi `, where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `cot(-x) = - cot(x) `then `cot (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `0` to `pi, cot (x)` is decreasing.

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = k pi` , where `k` is an integer.

`color(green)(✍️ ul "Range :")` all real numbers

`color(red)(✍️ ul "Period = ")` ` pi`

`color(green)(✍️ ul "x intercepts : ")` ` x = pi /2 + k pi `, where `k` is an integer.

`color(green)(✍️ ul "Symmetry:")` since `cot(-x) = - cot(x) `then `cot (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals of increase/decrease: ")` over one period and from `0` to `pi, cot (x)` is decreasing.

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = k pi` , where `k` is an integer.

`color(red)(✍️ ul "Domain :")` all real numbers except `pi/2 + k pi` , `n` is an integer.

`color(green)(✍️ ul "Range :")` ` (-oo , -1] U [1 , +oo)`

`color(red)(✍️ ul "Period = ")` `2 pi`

`color(green)(✍️ ul "y intercepts : ")` ` y = 1`

`color(green)(✍️ ul "Symmetry:")` since `sec(-x) = sec (x)` then `sec (x)` is an even function and its graph is symmetric with respect to the y axis.

`color(red)(✍️ ul "Iintervals 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)` .

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = pi/2 + k pi`, where `k` is an integer.

`color(green)(✍️ ul "Range :")` ` (-oo , -1] U [1 , +oo)`

`color(red)(✍️ ul "Period = ")` `2 pi`

`color(green)(✍️ ul "y intercepts : ")` ` y = 1`

`color(green)(✍️ ul "Symmetry:")` since `sec(-x) = sec (x)` then `sec (x)` is an even function and its graph is symmetric with respect to the y axis.

`color(red)(✍️ ul "Iintervals 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)` .

`color(green)(✍️ ul " Vertical asymptotes : ")` ` x = pi/2 + k pi`, where `k` is an integer.

`color(red)(✍️ ul "Domain :")` all real numbers except `k pi, k` is an integer.

`color(green)(✍️ ul "Range :")` ` (-oo , -1] U [1 , +oo)`

`color(red)(✍️ ul "Period = ")` ` 2pi`

`color(green)(✍️ ul "Symmetry:")` since `csc(-x) = - csc(x)` then `csc (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals 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)`.

`color(green)(✍️ ul " Vertical asymptotes : ")` `x = k pi`, where `k` is an integer.

`color(green)(✍️ ul "Range :")` ` (-oo , -1] U [1 , +oo)`

`color(red)(✍️ ul "Period = ")` ` 2pi`

`color(green)(✍️ ul "Symmetry:")` since `csc(-x) = - csc(x)` then `csc (x)` is an odd function and its graph is symmetric with respect the origin.

`color(red)(✍️ ul "Iintervals 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)`.

`color(green)(✍️ ul " Vertical asymptotes : ")` `x = k pi`, where `k` is an integer.