2.2a Right Triangle Trig!

Warm-up (IN)

Learning Objective: To learn and use all 6 trig functions and to solve unknown lengths of right triangles in standard position.

1. Convert to radians:a. b.

2. Convert to degrees:

a. b.

4. Find the area of the sector of a circle with the given measures: a.

3a.

2

3b.

4

135

5

12

6

270

12 m, radians

4r

a. 75 b. 30

2a. 0.5 m

NOTES

a

b

c SOH CAH TOAIN

PP

YP

OS

DJ

AN

YP

PP

DJ

sin 6 trig functions!

a

c

cos b

c

tan a

b

CAO SHA CHOOT

DJ

PP

PP

EC

YP

YP

DJ

SC

csc cosecant

sec

cot

secant

cotangent

c

a

c

b

b

a

Ex 1 - Find the value of all six trig functions given:

x

5

3

sin 3

5

cos 4

5

tan 3

4

csc

sec

cot

5

3

5

4

4

3

First find x…

Use Pythagorean theorem!

2 2 2a b c 23 2x 25

9 2x 252x 16x 4

4

Note… csc

sec

cot

1

sin1

cos1

tan

tan cossin

cot sincos

Given sinΘ = and cosΘ = , find the

remaining 4 trig functions

Ex 2 - 5

5

2 5

5

sin

cos

tan

csc

sec

cot

5

52 5

5

5

5

2 5

55

5

5

2 51

2

5

5

Must rationalize the denominator!

5

5 5

5

2 55

5 5

2

2

HW – p. 137 #11-17,21-23,28-32

Out – how do you find the 6 trig functions?

Summary - Wow, today was…

2.1 Quiz next time!!!