Thursday, March 4 Class

We went over quiz, noting several things...

First, when Mr. O’brien says to graph both and angle and its reference angle in standard position, the initial sides of both angles must be on the x-axis. Second, much as sin(90º-θ)= cosθ, sec(90º-θ)= cscθ

After going over the quiz, we went on to discuss the inverse trig functions.

y=sin^-1x

y=cos^-1x

y=tan^-1x

Notation problems: sin-1x does not equal (sinx)-1

Because of this potential confusion, there are other notations to represent the inverse functions:

arcsin (x)
arccos (x)
arctan (x)

We saw that on grapher, arcsin(x) isn’t a function. On our graphing calculators we saw the inverse trig function is a portion of the entire function. We consider the inverse trig functions to be a collection of all the points possible while still being a function.
The same applies to Cosine, which doesn’t pass the horizontal line test any more than the Sine function does. A single Tangent wave passes the horizontal line test, and that is all that’s graphed of the arctan function.
Of course, all three graphs look different from the originals, since they are inverse functions, and therefore have reverse (x,y) coordinates.

Here are links to the three inverse functions. This should help make their domains and ranges pretty clear.

http://www.math.rutgers.edu/~greenfie/mill_courses/math151a/gifstuff/arcsin.gif

http://www.intmath.com/Analytic-trigonometry/arccosx.gif

http://upload.wikimedia.org/wikipedia/commons/f/f6/Arctan_plot_real.png


arcsin (x)
Domain: [-1, 1]
Range: [-π/2, π/2]

arccos (x)
Domain: [-1,1]
Range: [0, π]

arctan (x)
Domain: [all real numbers]
Range: [-π/2,π/2 ]

Use of inverse functions: We can plug in coordinate points along the unit circle, and the inverse function gives the angle. It gives angles in quadrants where that particular function (sin, cos, tan) is positive.

Then we took the quiz, which brought us to the end of class.

According to the tags on the side, Collin has only done one scribe post, so now it's his turn for next class.