\( \def\dfrac#1#2{\displaystyle\frac{#1}{#2}} \def\solve#1{\begin{array}{rcl}#1\end{array} } \)

Home / 08 Trigonometric Functions / 50 Exploring Unit Circle And Trig Relations

While we have had an opportunity to use the Unit Circle as a tool for special angles, there is a lot more we can unpack within the unit circle. To begin with, we never fully investigated *why* the Tangent is \(\frac{{y}}{{x}}\) nor what the Cosecant and Secant refer to beyond the basic reciprocal identities. Moreover, there are even more powerful identities we can find by exploring various triangles that are formed within the Unit Circle. We will begin with drawing the tangent line to the circle at \(x=1\) and viewing the resulting triangles. Then we will solve for the sides using the standard right triangle trigonometric relationships.