For which angles is cosine positive? Select all that apply.

1. For which angle measures, \(\theta\), between 0 and \(2\pi\) radians is \(\cos(\theta) = 0\)? Label the corresponding points on the unit circle.

   

2. What are the values of \(\sin(\theta)\) for these angle measures?

Angle \(ABC\) measures \(\frac{\pi}{4}\) radian, and the coordinates of \(C\) are about \((0.71,0.71)\).

1. The measure of angle \(ABD\) is \(\frac{3\pi}{4}\) radians. What are the approximate coordinates of \(D\)? Explain how you know.
2. The measure of angle \(ABE\) is \(\frac{7\pi}{4}\) radians. What are the approximate coordinates of \(E\)? Explain how you know.

1. In which quadrant is the value of the \(x\)-coordinate of a point on the unit circle always greater than the \(y\)-coordinate? Explain how you know.
2. Name 3 angles in this quadrant.

Lin is comparing the graph of two functions \(g\) and \(f\). The function \(g\) is given by \(g(x) = f(x-2)\). Lin thinks the graph of \(g\) will be the same as the graph of \(f\), translated to the left by 2. Do you agree with Lin? Explain your reasoning.  

An original function is called \(f\). The function \(g\) is transformed from \(f\) using the following transformations, in this order:

• Stretch horizontally by a factor of \(\frac14\)
• Reflect over the \(y\)-axis
• Translate down 3

Write an equation for \(g(x)\) if \(f(x)\) is: 

1. \(x^3\)
2. \(e^x\)
3. \(\sqrt{x}\)