The tangent of an angle satisfies \(\tan(\theta) = 10\).

1. Which quadrant could \(\theta\) lie in? Explain how you know.
2. Estimate the possible value(s) of \(\theta\). Explain your reasoning.

Evaluate each of the following:

1. \(\tan\left(\frac{5\pi}{4}\right)\)
2. \(\sin\left(\frac{3\pi}{2}\right)\)
3. \(\cos\left(\frac{7\pi}{4}\right)\)

The sine of an angle, \(\theta\), in the second quadrant is \(0.6\). What is \(\tan(\theta)\)? Explain how you know. 

Triangle \(ABC\) is an isosceles right triangle in the unit circle.

A circle with center A at the origin of an x y plane. Point C lies on the outside of the curve, in the first quadrant, between the x and y axis. A point B is inside the circle, on the x axis, to the right of the origin. Segment A C is drawn. Segment B C is drawn. Angle C B A is labeled as a right angle.

1. Explain why \(\sin(A) = \cos(A)\).
2. Use the Pythagorean Identity to explain why \(2(\sin(A))^2 = 1\).

Triangle \(DEF\) is similar to triangle \(ABC\). The scale factor going from triangle \(DEF\) to triangle \(ABC\) is 3.

1. Explain why the length of segment \(AB\) is 3 times the length of segment \(DE\) and the length of segment \(BC\) is 3 times the length of segment \(EF\).
2. Explain why \(\sin(A) = \sin(D)\).