1. 1.4 Definition of the Trigonometric Functions OBJ:  Find the values of the six trigonometric functions of an angle in standard position

2. DEF:  Standard Position Angle with its vertex at the origin, initial side on the x-axis, and terminal side containing a point P with coordinates (x,y) P (x,y) y x 5 5 -5

3. Draw  in standard position. Choose any point P with coordinates (x, y) on the terminal side of  (P cannot be the vertex of  ) P (x,y)  y x 5 5 -5

4. y x 5 5 Draw the  to the x-axis at Q, forming ∆OPQ. PO = r > 0. x 2 + y 2 = r 2 P Q O

5. DEF: Trigonometric Functions X 2 + Y 2 = R 2 P (Opp) Y R (Hyp) (Adj) X SOHCAHTOA SYRCXRTYX Sin = Y Opp Csc = R Hyp R Hyp Y Opp Cos = X Adj Sec = R Hyp R Hyp X Adj Tan = Y Opp Cot = X Adj X Adj Y Opp y x 5 5 -5

6. All Students Take Calculus S A T C Sin All Tan Cos y x 5 5 -5 y x 5 5

7. 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 (8, 15) Sin = Y 15 Csc = R 17 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

8. 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=4 Cot = X = -3 3 -3 X -3 3 Y -4 4 -4 (-3,-4) y x 5 5 -5

9. 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

10. DEF:  Quadrantal angles TABLE OF VALUES OF THE SIX TRIGONOMETRIC FUNCTIONS OF QUAD.  S  0 90 180 270 360 450

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

12. EX:  Find the angles of smallest possible measure coterminal with the following angles: 900  y x 5 5 -5

13. EX:  Find the angles of smallest possible measure coterminal with the following angles: 900  900  – 720  180  y x 5 5 -5

14. 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