Transcript Day 3 Notes 1.4 Evaluating Trigonometric Expressions

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
-4sin 90+3cos 180+2csc 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 
5
y
x
-5
-5
5
EX:  Find the angles of smallest
possible measure coterminal
with the following angles: 908 
908 
– 720 
188 
5
y
x
-5
-5
5
EX:  Find the angles of smallest
possible measure coterminal
with the following angles: - 75 
5
y
x
-5
-5
5
EX:  Find the angles of smallest
possible measure coterminal
with the following angles: - 75 
360 
– 75 
285 
5
y
x
-5
-5
5