Introduction to Co-function Identities (Sine and Cosine only)

Introduction to Co-function Identities (Sine and Cosine only) Imagine that we are calculating

and

for the triangle below.

Using SOH-CAH-TOA, we can see that, relative to , the sides can be labeled like this:

But now, let’s say we want to calculate the sine of

and the cosine of .

This time, we can label our picture like this, relative to :

Those numbers look awfully familiar… that’s because we’ve seen them before! Look at the previous page and notice that:

This makes sense, because when we switch the angle that we are focusing on, the “opposite” and “adjacent” sides are also different. Remember, we’re talking about the side “opposite” or “adjacent” to the angle whose sine or cosine we are calculating. It turns out that this is true for EVERY pair of complementary angles. (A pair of complementary angles is a pair of angles whose measures add to 90 degrees.) This means that, for example, is often written like this:

and

. In trigonometry textbooks, this fact (

)

(

)

Practice: You try it! For each given trigonometric ratio, write an equivalent ratio. (The first one has been done for you.) 1)

___cos 65_____

2)

_____________

3)

_____________

4)

______________

5)

_____________

6)

_____________

7)

______________

8) 9) 10)

______________