Tuesday, November 9, 2010

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

Tuesday, November 2, 2010

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: -