Name: Period: Date:
Math Lab: Trig Identities Hexagon
Using the hexagon below, you will create a memory trick to learn the reciprocal, product/quotient, Pythagorean, and cofunction trig identities and how identities can be used to evaluate trig functions. An identity is an equation that is true for all x-values.
Reciprocal Identities
The two trig functions on any diagonal are reciprocals of each other. Write the six identities below:
Product Identities
Along the outside edges of the hexagon, any trig function equals the product of the functions on the adjacent vertices. Write the six identities below:
Quotient Identities
Along the outside edges of the hexagon, any trig function equals the quotient of the functions on the next two consecutive vertices in either direction. Write the identities below in two equivalent forms for each:
= = =
= = =

Pythagorean Identities
For each shaded triangle, the upper left function squared plus the upper right function squared equals the bottom function squared. Write the identities below in three equivalent forms for each:
Even and Odd Identities
Recall that functions are considered even or odd if their graphs have y-axis or origin symmetry respectively.
Algebraically, holds true for all even functions and holds true for all odd functions. Write the identities below.
Cofunction Identities
The trig functions cosine, cotangent, and cosecant on the right of the hexagon are the cofunctions of sine, tangent, and secant on the left, respectively. So, sine and cosine are cofunctions; hence the “co” in cosine.
Cofunction identities are created from and being a pair of complementary angles.
These identities can be verified with even/odd identities and transformation rules for phase shifts & reflections.
Write the identities below:
Practice
Given and , find the other six trig functions. Show your work.