Tuesday, January 15, 2008


Well back once again for another scribe. Well class started off very cold, the classroom itself was freezing. Although class started as usually and we began with a couple inverse trig functions. They started off being on the easier side, like sin^-1(sin(pi/3)) in which case sin was in the perfect quadrant, so arcsin was the original value of sin, (pi/3).

Then they became a little harder like, arcsin(sin(5pi/4)) in which case 5pi/4 is -2^(.5)/2. So we know that Sin lives in quadrants 1&4, so arcsin(-2^(.5)/2) would be in quadrants 3&4, so quadrant four will be picked in which case the arcsin(-2^(.5)/2) in quadrant 4 is (7pi/4 ).

Next we went in the opposite direction, which was by taking a length and finding its arc value, then in which case the trig value wanting to be determined will be found. An example is : cos(arctan 1), in which case we work backwards. We first find the arctan of 1, which is pi/4. Then we want to find the trig value, cos of pi/4. The value of cos(pi/4) is 2^(.5)/2. So the answer is 2^(.5)/2.

Next we went to something completely new, and that was to find a length that was not common and find its arc value. Here is an example: cot(arcsin(2/3)), the first thing we do is solve as a function by using x. So it becomes sin(arcsin(2/3)) = sin x ----> (2/3) = sin x. So after we find this we solve using Pythagoras's theorem by using the length and the trig function given. opp=2, hyp=3, and by solving adj= 5^(.5). So now bring in the other trig value of the equation, cot which is adj/opp it solves as 5^(.5)/2, which is the final answer to that question.

Just before the end of class Mr.K asked the class to draw the graphs of arccos(x), arcsin(x), and arctan(x). So just something to remember, the graph of arc trig functions are its Cap trig graphs reflected over the function y=x. due to the fact that if you do not use the Cap trig graphs reflected over the function y=x, the arc trig function would not be a function as it would fail the vertical line test. So remember that piece of advice, as Mr. K said in class today with the use of Star Trek.

Mr.K did not assign any homework today, so we have the night off. Tomorrow's scribe is going to be Tim_Math_y.

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