2.4 Trig Functions of General Angles

Warm-up (IN)

Learning Objective: To find all 6 trig functions of a resulting triangle given a point anywhere in the Cartesian coordinate plane and to identify characteristics of the four quadrants, leading to the understanding of which trig functions are positive and negative in each quadrant.

1. Did you remember all of the unit circle?2. What do you think you will most likely forget for

the Chapter 2 test?

NOTES

( , )a b

Given:

r

You can make a right triangle

r

ref

( , )a b

(0,0)

where 2 2r a b Ex 1 – Find all 6 trig functions of a positive angle, Θ, if (4, -3) is a point on its terminal side.

4

3

224 3r

25r 5r 5

sin 3

5

cos 4

5

tan 3

4

csc 5

3

sec 5

4

cot 4

3

a

b

Two angles in standard position are coterminal if they have the same terminal side.

135

225

45765

Ex 2 – Use coterminal angles to find the exact value of each trig function

a. sin 390 sin 30 1

2

7b. sec

4

sec4

2

c. cos 420 cos60 1

2 d. csc 270 csc90 1

9e. tan

4

tan4

1

Signs of the trig functions in each quadrant...

All Seniors Take Calculus! , ,

, ,

Ex 3 – a. If sinΘ and cosΘ < 0, what quadrant does Θ lie?

3

b. If sinΘ>0 and tanΘ < 0, what quadrant does Θ lie?

2

HW – p. 162 #11-14, 19-25,33-38

Out – Find the exact value of cos480º

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