Hi, everyone.
In Advanced Algebra, we discussed 8-4: Roots and Zeroes. We mentioned the fact that every polynomial function has at least one root: real or imaginary. The roots can take the form: a + bi. For instance, the roots to x^2 + 1 = f(x) are +i and -i. They appear in the form 0 + i and 0 - i. This means that (x - (0 - i))(x -(0 + i)) = x^2 + 1 = f(x). We also generated polynomial functions from roots. That is, if x = -2, 3 and 4i. Then the polynomial function (in factored from) looks like (x + 2)(x - 3)(x - (0-4i))(x - (0+4i)), a quartic function. The homework is on pg. 507 #32-40.
In Geometry, we discussed 8-4: Angles of Elevation and Depression. Using trigonometric ratios, we determined the values of angles or side measures in word problems.
The example used in class is the following....watch the clip
http://www.youtube.com/watch?v=eiL31ZBxoy8
Looking at the clip on youtube...Look at time 1:00. As Magneto is meters and seconds away from lowering the bridge on the guards, he thinks-"I wonder what the angle of depression is to the guard as I am about to finish them!" The image of the bridge and Alcatraz forms a special image. The distance from Magneto's eye line to the guard's eye line is 1,000 ft (the hypotenuse). Magneto is 100 ft above the guard (the altitude). Based on this information, you can use 'sine of x' to figure the problem out. So, sin (x) = (100/1,000). Once you take the inverse of each side, sin^-1(100/1,000) = x -which is the angle of depression. Make sure your calculator is in degrees and not radians. The homework is pg. 422 #22-25.
Be Safe. Please, BE SAFE!
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