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# Right Triangles and Trigonometry

# Sine, Cosine, and Angles

It's also important to know the relationship of sine and cosine. We don't mean to pry into their personal lives, but it really is crucial. In order to find out what their relationship is, exactly, we can do a few calculations.

We already know that sin *A* = ^{a}⁄_{h} and cos *A* = * ^{b}*⁄

*but what about ∠*

_{h}*B*? Remembering SOHCAHTOA, we can see that sin

*B*=

*⁄*

^{b}*and cos*

_{h}*B*=

*⁄*

^{a}*. Was that the sound of the earth gasping? Yes, that's right.*

_{h}sin *A* = cos *B*

cos *A* = sin *B*

Wait. It gets better. We know that there are 180° in a triangle, but the 90° takes half of that out of the equation. That means *A* + *B* = 90°. Using that relationship, we can clarify our sine-cosine relationship.

sin *A* = cos(90° – *A*)

cos *A* = sin(90° – *A*)

This means that sine and cosine are *complementary* trig functions (because the angles are complementary). Like the two main characters in any Nicholas Sparks novel, they complete each other.

Also relevant to this chapter are angles of and depression. They both involve looking at cats. Awww.

**Angles of elevation** are the angles from a horizontal to an upward line of sight and **angles of depression** are from a horizontal to a downward line of sight. Like looking at a cat on top of a bookcase or sunbathing on the floor.