Trigonometric RatiosSOH CAH TOA

If we are given a point, P(x, y), wewill have 2 of the three distancesthat we need to know. We will stillneed to figure out the distance tothe origin, r. The pythagoreantheorem will help us here.

` P(3, 4)

E s hu

sinktank

cask

2 67so I

I sin 30 01

t.s.izo.hrcos30 adyip

Bcos 30 a

2

In Quadrant 1 (Q1) the angle and the reference angle are thesame. For any other quadrant you will use the reference angle todetermine the value of the trigonometric ratio then you will need touse logic (or memorization) to determine the sign of the angle.

Let’s do one in each quadrant.Find the sine, cosine, and tangent for in each graph.

5 n 45 1sin 45 12 th vz

cos 45 tus 45 In

tan 45 1Cos 135 Luz

ta 135 1

Point, P(-8, 15) lies on the terminal arm of an angle , in standardposition. Determine the exact trig ratios for .

Si 225 to sin 315

a us I 3ton 225 1

S A

IC L

A ta.o

since IIT C cos O g

r Ft17

The point, P(-5, -12) lies on the terminal arm of an angle in standardposition. Determine the exact trigonometric ratios for

.

Determine the exact value of .

since

g A Caso Is

y.jotano

T C

riff13

S A Cos 135 tr

Cos 45 tr

T C

Suppose is an angle in standard position with terminal arm in Q3,

and . What are the exact values of ?

Determine the trig ratios for:

HW:2.2:2, 3, 5, 9, 11, 14, 20

S ASino IsEso Zta O Iz

t c

5 Co 1

3

Hot a

sin 90 1cos 90 0

fo 1sin ycos x