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1.4 Definition of the Trigonometric Functions

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

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1.4 Definition of the Trigonometric Functions

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

  2. 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 5 x -5 -5 5 DEF:  Standard Position

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

  4. x2 + y2 = r2 P Q O y 5 x -5 -5 5 Draw the  to the x-axis at Q, forming ∆OPQ. PO = r > 0.

  5. X2 + Y2 = R2 P (Opp) Y R (Hyp) (Adj) X SOHCAHTOA SYRCXRTYX Sin = Y OppCsc = RHyp R Hyp Y Opp Cos = XAdjSec = RHyp RHypX Adj Tan = YOppCot = XAdj X Adj YOpp y 5 x -5 -5 5 DEF: Trigonometric Functions

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

  7. y y 5 5 x x -5 -5 -5 -5 5 5 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 = Y15 Csc = R17 R 17 Y 15 Cos = X8Sec =R17 R 17 X 8 15 Tan = Y15 Cot = X8 X 8 Y 15 8

  8. y 5 x -5 -5 5 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 5Y -4 Cos = X = -3Sec =R= 5 R 5X -3 Tan = Y= -4=4Cot = X=-3 3-3 X -3 3 Y -44 -4 (-3,-4)

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

  10. DEF: Quadrantal angles TABLE OF VALUES OF THE SIX TRIGONOMETRIC FUNCTIONS OF QUAD.  S

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

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

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

  14. DEF: Quadrantal angles TABLE OF VALUES OF THE SIX TRIGONOMETRIC FUNCTIONS OF QUAD.  S

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