Graphing Inverse Trigonometric Functions

Graphing inverse Trigonometric functions is pretty much like taking a part of a trigonometric function that passes the horrizontal line test, and flipping it over the line y=x

this is what arctan looks like....

tanx                arctan

D:(-pi/2,pi/2)                  D:(-infin,infin)

R:(-infin,infin)                   R:(-pi,pi)

this is what arcsin looks like (just the red part)...

sinx                arcsinx

D:(-pi/2,pi/2)                  D:(-1,1)

R:(-1,1)                   R:(-pi/2,pi/2)

and this is what arccos looks like (just the black part);

cosx                arccosx

D:(0,pi)                  D:(-1,1)

R:(-1,1)                   R:(0,pi)

Remember, the output of an inverse trig function is an ANGLE

Graphing of Trigonometric Functions

Today in class we learned how to graph all the trigonometric functions.

y = sin x

Domain: all real numbers

Range: [-1, 1]

Period: 2π

y = cos x

Domain: all real numbers

Range: [-1, 1]

Period: 2π

y = tan x

Domain: all, x can't equal π/2 + n(π)

Range: (-∞, ∞)

Period: π

y = csc x = 1/ sin x

Domain: all x can't equal n(π)

Range: (-∞, -1] and [1, ∞)

Period: 2π

y = sec x = 1/ cos x

Domain: all x can't equal π/2 + n(π)

Range: (-∞, -1] and [1, ∞)

Period: 2π

y = cot x = 1/tan x

Domain: all x can't equal n(π)

Range: (-∞, ∞)

Period: π

4.4 Trigonometric Functions of Any Angle

Today in class we learned how to find the six trigonometric functions for any angle.
Defenitions of Trigonometric Functions of Any Angle
Let θ be an angle in standard position with (x,y) a point on the terminal side of θand r = √x^2+y^2 = 0.

sinθ = y/r                 cosθ = x/r
tanθ = y/x                cotθ= x/y
secθ = r/x                cscθ = r/y

To evluate these trigonometric functions, when given a point on the terminal side of θ, plug in the coordinates of that point to find r. Then plug in r and the afforementioned cordinates for the above defenitions and have fun.


We also discussed in class the signs of the trigonometric functions in each quadrant.

Quadrant I            Quadrant II            Quadrant III            Quadrant IV
sinθ: +                    sinθ: +                      sinθ: -                        sinθ: -
cosθ: +                   cosθ: -                     cosθ: -                       cosθ: +
tanθ: +                    tanθ: -                      tanθ: +                       tanθ: -