The mythical Hydra was a beast that was very difficult to kill -- if you cut off its head, it grew 12 new ones to replace it. If you cut off one of those heads, 12 more would grow... if you cut off one of those, 12 more would grow ....

The ...

1. Prove that $sin\theta (csc\theta - sin\theta) = cos^2 \theta$

1. Given the distance between a gunner and a spotter, and the angles each measures between the line between them and the respective lines to their target, compute the dstance between the gun and the target.

1. Suppose a tire of radius 0.5 meters is spinning at the rate of 2 radians per second. Imagine a line drawn through the center of the tire (using chalk) that is initially parallel with the ground. Sketch a graph showing the height of the end of that line as ...

1. Without a calculator, consider what happens to the function f(x) = cos(x) when the underlying unit circle has a radius of 4. Express a new function that gives the x-coordinate of points on the circle at given radii x, and sketch the function neatly showing the value at standard ...

1. Calculators are NOT permitted on this quiz.

Write down the values of the sine and the cosine functions when the following angles are input:

($0, \frac{\pi}{4}, \frac{\pi}{2}, \frac{3\pi}{4}, \pi, \frac{5\pi}{4}, \frac{3\pi}{2}, \frac{7\pi}{4}$),

1. The following are lengths of sides of right triangles. Find the length of the missing side:
   1. 1, x, 2
   2. 1, 1, x

2. If a wheel of radius 10 centimeters turns through 10.7 revolutions, how far does the wheel travel, and by what angle (in radians) does it turn?

1. $f(x) = 2x + 5$, $g(x) = x - 2$.
   1. What is $(f \circ g)(x)$?
   2. What is $(g \circ f)(x)$?
   3. What are the domain and range of the functions in a and b?

1. What are the domain and range of the function $f(x) = \frac{\sqrt{x+3}}{x+2}$?
2. Give a function that has the same domain, but a different range from the function $g(x) = -\sqrt{x - 4}$
3. The function $t(r) = \frac{h\pi r^2}{R}$ models the time ...

1. What values of $x$ are possible inputs to the function $f(x) = \sqrt{x + 2}$? What are the possible outputs of this function?
2. Give another function that has the same set of possible inputs, but a different set of possible outputs.
3. Give another function that has the same set of ...

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