A common lesson early in precalculus is determining whether or not a graph shows a function. A simple way to check this is to perform the vertical line test. Place a pencil or other straight object on the graph with the ends of the object pointing up and down. Drag the object across the graph. If at any point there are multiple values on the y-axis for a single value on the x-axis, it isn't a function.
The horizontal line test can be used to determine if a function has an inverse. Perform this test by placing a straight object across the graph with the ends of the object facing to the sides. As you drag the object up and down the graph, look for multiple values on the x-axis for a single value on the y-axis, which would indicate that there is no inverse of the function.
Sine, cosine, tangent and their reciprocals can be found by remembering six simple identities that relate to the sides of a triangle but are less complicated than the SOH-CAH-TOA method. These identities are: Sine = y/r, cosine = x/r, tangent = y/x, cotangent = x/y, secant = r/x, cosecant = r/y
These identities relate to a triangle, with "x" and "y" being the sides and "r" being the hypotenuse. For example, with tangent 1/2, x is equal to 2 and y is equal to 1. From that you can find cotangent, which is x/y, 2/1, or 2 in this case.
The unit circle is used with sine, cosine and tangent problems as well as determining angles. There is a simple way to remember these angles. A 30-degree angle is π/6, and the x/y coordinates are √3/2 and 1/2. A 45-degree angle is π/4 and the x/y coordinates are √2/2 and √2/2. A 60-degree angle is π/3 and the x/y coordinates are 1/2 and √3/2. Use these to determine the remaining values. For example, the angle 150 is five times angle 30, so it is 5π/6. Imagine the unit circle on a graph with the center being at the graph's origin. In quadrant 1, both x and y are positive, in quadrant 2, x is negative, in quadrant 3, both are negative and in quadrant 4, y is negative. So angle 150 would have the coordinates -√3/2 and 1/2.