Day 3 Notes

1.4 Definition of the Trigonometric Functions

OBJ: Evaluate trigonometric expressions involving quadrantal angles

OBJ: Find the angle of smallest possible measure coterminal with a given angle

13) cos 90 º + 3 sin 270 º

+ 3( )

0 + 3( )

0 + 3(-1)

-3

15) 3 sec 180 – 5 tan 360

3( ) – 5( )

3(-1) – 5( )

3(-1) – 5( )

3(-1) – 5(0)

-3

17) tan360+ 4sin180+ 5cos2180

+ 4( ) + 5( )2

0 + 4( ) + 5( )2

0 + 4( ) + 5( )2

0 + 4(0) + 5( )2

0 + 4(0) + 5(-1)2

5

19) sin 2 180 + cos 2 180

+ ( )2

0 + ( )2

0 + (-1)2

1

21)sec2180- 3sin2360+ 2cos180

( )2 – 3( )2 + 2 ( )

(-1)2 – 3(0)2 + 2 (-1)

(-1)2 – 3(0)2 + 2 (-1)

(-1)2 – 3(0)2 + 2 (-1)

1 – 2

-1

23)2sec2360-4sin290+5cos180

2( )2 – 4( )2 + 5( )2(1)2 – 4( )2 + 5( )2(1)2 – 4(1)2 + 5( )2(1)2 – 4(1)2 + 5(-1)2 – 4 + 5

3

-4sin 90+3cos 180+2csc 270

-4( ) + 3 + 2

-4(1) + 3 + 2

-4(1) + 3-1 + 2

-4(1) + 3-1 + 2-1

– 4 + 3 + 2

1

DEF: Coterminal Angles

Angles with the same initial side and

the same terminal side

EX: Find the angles of smallest possible measure coterminal

with the following angles: 908

y

x

5

5

-5-5

EX: Find the angles of smallest possible measure coterminal

with the following angles: 908 908 – 720 188

y

x

5

5

-5-5

EX: Find the angles of smallest possible measure coterminal

with the following angles: - 75

y

x

5

5

-5-5

EX: Find the angles of smallest possible measure coterminal

with the following angles: - 75 360 – 75 285

y

x

5

5

-5-5