Graphing Trigonometric Functions with Domain and Range

Key Questions

  • Answer:

    Using a graphing calculator: MODE must be in radians

    Explanation:

    Using a graphing calculator: MODE must be in radians.

    On a TI graphing calculator, with the standard zoom, #Y1 = sin(x)#:

    graph{sin(x) [-10.04, 9.96, -5.16, 4.84]}

    On a TI graphing calculator, with the standard zoom, #Y1 = cos(x)#:

    graph{cosx [-10.04, 9.96, -5.16, 4.84]}

    On a TI graphing calculator, with the standard zoom, #Y1 = tan(x)#:

    graph{tan x [-10.04, 9.96, -5.16, 4.84]}

    On a TI graphing calculator, with the standard zoom, #y = sec(x): Y1 = 1/(cos(x))#:

    graph{1/(cos x) [-10.04, 9.96, -5.16, 4.84]}

    On a TI graphing calculator, with the standard zoom, #y = csc(x): Y1 = 1/(sin(x))#:

    graph{1/(sin x) [-10.04, 9.96, -5.16, 4.84]}

    On a TI graphing calculator, with the standard zoom, #y = cot(x): Y1 = 1/(tan(x))#:

    graph{1/(tan x) [-10.04, 9.96, -5.16, 4.84]}

  • Answer:

    #sin(x)#, #cos(x)#, #tan(x)#, #csc(x)#, #sec(x)#, #cot(x)#.

    Explanation:

    #cos(x)=sin(pi/2-x)#

    #tan(x)=frac{sin(x)}{cos(x)}#

    #csc(x)=1/sin(x)#

    #sec(x)=1/cos(x)#

    #cot(x)=1/tan(x)#

  • Given a right triangle, select a vertex where the hypotenuse and one of the legs meet.

    The angle #theta# created by this two sides will be used as a reference point

    The side that formed the angle #theta# together with the hypotenuse will be referred to as #adjacent# (side adjacent to the angle). The other side will be referred to as #opposite# (side opposite the angle)

    The ratio between the #opposite# and the #"hypotenuse"# is called #"sine" (sin#). The inverse of this ratio is called #"cosecant" (csc#)

    #sin theta = "opposite" / "hypotenuse" #

    #csc theta = "hypotenuse" / "opposite" = 1 / sin theta#

    The ratio between the #adjacent# and the #"hypotenuse"# is called "cosine". The inverse of this ratio is called "secant"

    #cos theta = "adjacent" / "hypotenuse" #

    #sec theta = "hypotenuse" / "adjacent" = 1 / cos theta#

    The ratio between the #opposite# and the #adjacent# is called
    #"tangent"#. The inverse of this ratio is called #"cotangent"#

    #tan theta = "opposite" / "adjacent"#

    #cot theta = "adjacent" / "opposite" = 1 / tan theta#


    For example, in a 30-60-90 triangle

    #sin 30 = 1 / 2#
    #cos 30 = 3^(1/2)/2#
    #tan 30 = 1 / 3^(1/2)#
    #csc 30 = 2#
    #sec 30 = 2/3^(1/2)#
    #cot 30 = 3^(1/2)#

    #sin 60 = 3^(1/2)/2#
    #cos 60 = 1 /2 #
    #tan 60 = 3^(1/2)#
    #csc 60 = 2/3^(1/2)#
    #sec 60 = 2#
    #cot 60 = 1 / 3^(1/2)#

Questions