SP#7: Unit Q Concept 2: Finding All Trig Functions When Given One Trig Function and Quadrant

This SP7 was made in collaboration with Sarahi Leal. Please visit the other fantabulous, supercalifragilisticexpialidocious posts on her blog by going here.

Solving with Identities:

Solving with SOH CAH TOA: 

The idea we want you to formulate is that there are two ways to find these trig functions: using identities and using SOH CAH TOA. When dealing with identities, it is always best to remember to know WHERE the unknown triangle falls in. As you can see in our very first step, we determined what quadrant the triangle is in, just by knowing what quadrants certain trig functions are positive and such. Another good thing to remember, especially as we deal with identities more and more, is that when you square root a trig function (as seen in #4 of "Solving with Identities"), you will end up with two possible answers because it is both negative and positive. However, we were able to conclude that it was positive because sine and cosecant are positive within Quadrant II. Always remember these little nuances because they do help in making these types of problems easier.