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. Go to the following survey
2. Fill it out with your thoughts on the class. I REALLY appreciate honest feedback, and will make changes next term in response to your thoughts, so please take time to honestly reflect on your experience. The long-response questions near the bottom are the most helpful ...

Logarithms

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.

Trignometric identities

Graphing trigonometric functions

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:

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

Unit circle and angles

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?

Try out geogebra

Angles!

Quadratic functions

Composition of functions

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?

Functional notation and composition

More functions