1. Day 2 and Day 3 notes

2. 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

3. 13) cos 90 º + 3 sin 270 º + 3( ) 0 + 3( ) 0 + 3(-1) -3

4. 15) 3 sec 180  – 5 tan 360  3( ) – 5( ) 3(-1) – 5( ) 3(-1) – 5(0) -3

5. 17) tan360  + 4sin180  + 5cos 2 180  + 4( ) + 5( ) 2 0 + 4( ) + 5( ) 2 0 + 4(0) + 5( ) 2 0 + 4(0) + 5(-1) 2 5

6. 19) sin 2 180  + cos 2 180  + ( ) 2 0 + ( ) 2 0 + (-1) 2 1

7. 21)sec 2 180  - 3sin 2 360  + 2cos180  ( ) 2 – 3( ) 2 + 2 ( ) (-1) 2 – 3(0) 2 + 2 (-1) 1 – 2

8. 23) 2sec 2 360  -4sin 2 90  +  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

9. -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

10. DEF:  Coterminal Angles Angles with the same initial side and the same terminal side

11. EX:  Find the angles of smallest possible measure coterminal with the following angles: 908  y x 5 5 -5

12. EX:  Find the angles of smallest possible measure coterminal with the following angles: 908  908  – 720  188  y x 5 5 -5

13. EX:  Find the angles of smallest possible measure coterminal with the following angles: - 75  y x 5 5 -5

14. EX:  Find the angles of smallest possible measure coterminal with the following angles: - 75  360  – 75  285  y x 5 5 -5

15. EX 4  Find the values of the six trigonometric functions for an angle of 90 . P 39 Sin = Y = 1 Csc = R = 1 R 1 Y 1 (0, 1) Cos = X = 0 Sec = R = 1 = Ø R 1 X 0 Tan = Y = 1 = Ø Cot = X = 0 X 0 Y 1 y x 5 5 -5

16. DEF:  Quadrantal angles TABLE OF VALUES OF THE SIX TRIGONOMETRIC FUNCTIONS OF QUAD.  S  Sin  Cos  Tan  Cot  Sec  Csc  0010Ø1Ø 9010Ø0Ø1 18000Ø Ø 2700Ø0Ø 360010Ø1Ø 45010Ø0Ø1

17. EX: 1  The terminal side of an angle  in standard position goes through the point ( 8, 15 ). Find the values of the six trigonometric functions of  P 35 Sin = Y 15 Csc = R 17 (8, 15) R 17 Y 15 Cos = X 8 Sec = R 17 R 17 X 8 15 Tan = Y 15 Cot = X 8 X 8 Y 15 8 y x 5 5 -5 y x 5 5

18. EX 2  The terminal side of an angle  in standard position goes through the point (-3, - 4 ). Find the values of the six trigonometric functions of . P 36 Sin = Y = -4 Csc = R = 5 R 5 Y -4 Cos = X = -3 Sec = R = 5 R 5 X -3 Tan = Y = 4 Cot = X = -3 -3 X -3 Y 4 -4 (-3,-4) y x 5 5 -5