Mr. Unit Circle

The unit circle has coordinates at various points but the main coordinates are (1,0), (0,1), (-1,0), and (0,-1). (1,0) is zero in radians and (0,1) is pi/2 in radians and (-1,0) is pi in radians and (0,-1) is 3pi/2 in radians. (Cosine, sine) is cosine for x and sine for y. The first quadrant is positive for cosine and sine, the second quadrant is negative for cosine and positive for sine, the third quadrant is positive for cosine and negative for sine, and the fourth quadrant is positive for cosine and negative for sine. The unit circle is helpful for figuring out if a triangle is 45, 45, 90 triangle or 30, 60, 90 triangle. The unit circle is also the simplest way of finding lengths and angles of triangles. All sine, cosine, and tangent points have similar cordinates. 

Law of Sines/ Cosines

The Law of Sines establishes a relationship between the angles and the side lengths of triangle ABC. In total there are three sines. Another important relationship between the side lengths and the angles of a triangle is expressed by the Law of Cosines. The expression itself involves a single cosine, but by rotation or symmetry similar formulas are valid for other angles. Also cosine unlike sine changes, it's sign in the range from 0 degrees to 180 degrees of valid angles of a triangle. Sine is always positive in this range, cosine is positive up to 90 degrees where it becomes zero and is negative afterwards.