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(a) when looking from the positive end of an axis of rotation, is positive
rotation clockwise (CW) or counterclockwise (CCW)?
(b) when looking from the negative end of an axis of rotation, is positive
rotation CW or CCW?
In a right-handed coordinate system:
(c) when looking from the positive end of an axis of rotation, is positive
rotation CW or CCW?
(d) when looking from the negative end of an axis of rotation, is positive
rotation CW or CCW?
7. Compute the following:
5
5
5
4
100
(e)
8
(a)
i
(b)
2i
(c)
2i
(d)
7(i + 1)
i
i=1
i=1
i=1
i=0
i=1
8. Convert from degrees to radians:
(a) 30
o
(b) −45
o
(c) 60
o
(d) 90
o
(e) −180
o
(f) 225
o
(g) −270
o
(h) 167.5
o
(i) 527
o
(j) −1080
o
9. Convert from radians to degrees:
(a) −π/6
(b) 2π/3
(c) 3π/2
(d) −4π/3
(e) 2π
(f) π/180
(g) π/18
(h) −5π
(i) 10π
(j) π/5
10. In The Wizard of Oz, the scarecrow receives his degree from the wizard and
blurts out this mangled version of the Pythagorean theorem:
The sum of the square roots of any two sides of an isosceles
triangle is equal to the square root of the remaining side.
Apparently the scarecrow's degree wasn't worth very much, since this
“proof that he had a brain” is actually wrong in at least two ways.
9
What
should the scarecrow have said?
8
There is a well-known story about the mathematician Karl Friedrich Gauss solving
this problem in only a few seconds while a student in primary school. As the story goes,
his teacher wanted to occupy the students by having them add the numbers 1 to 100
and turn in their answers at the end of class. However, mere seconds after being given
this assignment, Gauss handed the correct answer to his teacher as the teacher and the
rest of the class gazed in astonishment at the young Gauss.
9
Homer Simpson repeated the same jibberish after putting on a pair of glasses found
in a toilet. A man in a nearby stall corrected him on one of his errors. So if you saw
that episode of The Simpsons, then you have a headstart on this question, but not the
whole answer.
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