2) Find the measure of angle CAB in radians. Explain how you know.
I got this question wrong because I didn't see the arc length so I didn't know how to do the problem.
Now that I see the arc length, here is my answer:
The arc length formula for radians is the central angle*radius, therefore we can derive the formula that the central angle is the arc length/radius.
Therefore, since the arc length is 15 cm and the radius is 5 cm, the measure of the central angle is 3 radians.
7) For this problem I forgot to put in the angle measure of each reference angle, so here are the angle measures.
a) The reference angle for 500 degrees is 40 degrees, since the 500 degree angle goes around the cirlce once and then goes around an additional 140 degrees, making its terminal side in the 2nd quadrant. The acute angle formed with the x-axis is therefore 40 degrees.
b) The reference angle for -5pi/3 is pi/3 because the angle -5pi/3 lies in the first quadrant, pi/3 radians away from the x-axis.
I missed one critical day during this section so I didn't ever fully learn the formulas on my own, which made this unit difficult for me.
Friday, November 9, 2012
Saturday, November 3, 2012
Functions and Critical Values Test Corrections
6) Given the function y=20x^7-10x^3/5x^3
a) State the end behavior of the function and explain how you can determine the end behavior without graphing the function.
What I had:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches negative infinity
If the greatest exponent is odd and the leading coefficient is positive, the above will be the end behavior.
Why this is wrong:
I did not simplify the function.
Simplified, the function is 4x^4-2.
The right answer:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches infinity
If the greatest exponent is even and the leading coefficient is positive, the above will be the end behavior.
b) State the intervals where the function is increasing and decreasing.
What I had: increasing for all real numbers
Why this is wrong: I put the equation into the calculator without parentheses around the numerator and denominator.
The right answer: decreasing {x/0>x} increasing {x/0<x}
This unit was fine as it was pretty much a review from last year, but I didn't ever memorize the end behavior rules.
a) State the end behavior of the function and explain how you can determine the end behavior without graphing the function.
What I had:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches negative infinity
If the greatest exponent is odd and the leading coefficient is positive, the above will be the end behavior.
Why this is wrong:
I did not simplify the function.
Simplified, the function is 4x^4-2.
The right answer:
end behavior: as x approaches infinity f(x) approaches infinity
as x approaches negative infinity f(x) approaches infinity
If the greatest exponent is even and the leading coefficient is positive, the above will be the end behavior.
b) State the intervals where the function is increasing and decreasing.
What I had: increasing for all real numbers
Why this is wrong: I put the equation into the calculator without parentheses around the numerator and denominator.
The right answer: decreasing {x/0>x} increasing {x/0<x}
This unit was fine as it was pretty much a review from last year, but I didn't ever memorize the end behavior rules.
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