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1.5 Using the Definitions of the Trigonometric Functions

1.5 Using the Definitions of the Trigonometric Functions. OBJ: • Give the signs of the six trigonometric functions for a given angle OBJ: • Identify the quadrant or quadrants for angles satisfying given conditions. y. y. 5. 5. x. x. -5. -5. -5. -5. 5. 5.

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1.5 Using the Definitions of the Trigonometric Functions

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  1. 1.5 Using the Definitions of the Trigonometric Functions OBJ: • Give the signs of the six trigonometric functions for a given angle OBJ: • Identify the quadrant or quadrants for angles satisfying given conditions.

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

  3. 19)sin >0, cos <0 I, II I, IIII, III 21)sec <0, csc <0 II, III II, IIIIII, IV 23)Sin <0, cos >0 III, IV III, IV I, IV Identify the quadrant or quadrants for the angles satisfying the following conditions.

  4. 25)tan <0, cot <0 II, IV II, IVII, IV 27) sin  > 0 I, II 29) tan  > 0 I, III Identify the quadrant or quadrants for the angles satisfying the following conditions.

  5. Give the signs of the six trigonometric functions for each of the following angles. Sin|Cos|Tan|Cot|Sec|Csc 31) 74  + | + | + | + | + | + | 33) 183  – | – | + | + | – | – | 35) 302  – | + | – | – | + | – |

  6. Give the signs of the six trigonometric functions for each of the following angles. Sin|Cos|Tan|Cot|Sec|Csc 37) 406  + | + | + | + | + | + | 39) -82 – | + | – | – | + | – | 41) -121  – | – | + | + | – | – |

  7. 1.5 Using the Definitions of the Trigonometric Functions OBJ: • Find the other trigonometric functions, given one of them and quadrant information

  8. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information EX: cos  = - 3 ,  in Q II; Find sin  4

  9. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information EX: cos  = - 3 ,  in Q II; Find sin  4 x2 + y2 = r2 (- 3 )2 + y2 = 42 3 + y2 = 16 4 y2 = 13 - 3 y =  13 sin  =  13 4

  10. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 61) sin  = 2 ,  in Q II; Find cos  3

  11. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 61) sin  = 2 ,  in Q II; Find cos  3 x2 + y2 = r2 x2 + 22 = 32 x2 + 4 = 9 2 3 x2 = 5 x = - 5 cos  = - 5 3

  12. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 63) cot  = -1,  in Q IV; Find csc  2

  13. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 63) cot  = -1,  in Q IV; Find csc  2 x2 + y2 = r2 12 + (-2)2 = r2 1 + 4 = r2 5 = r2 15 = r 2 csc  = 5 -2

  14. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 65) tan  = 7,  in Q III; Find sec  3

  15. y 5 x -5 -5 5 Find the following trigonometric function, given a trigonometric function & quadrant information 65) tan  = 7,  in Q III; Find sec  3 x2 + y2 = r2 (-3)2 + (- 7)2 = r2 9 + 7 = r2 -3 16 = r2 4 = r - 7 sec  = 4 -3

  16. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 69) cos  = - 3 ,  in Q III 5

  17. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 69) cos  = - 3 ,  in Q III 5 x2 + y2 = r2 (-3 )2 + y2 = 52 y = - 4 -3 5

  18. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 73) csc  = 2 ,  in Q II

  19. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 73) csc  = 2 ,  in Q II x2 + y2 = r2 x2 + 12 = 22 x2 + 1= 4 x2= 3 1 2 x = -3

  20. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 77) sin  = -5 , cos  > 0 6

  21. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 77) sin  = -5 , cos  > 0 6 x2 + y2 = r2 x2 + (-5)2 = 62 x2 + 25= 36 x2 = 11 x = 11 6 -5

  22. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 79) cot  =  3 , sin  > 0 8

  23. y 5 x -5 -5 5 Find all the other trigonometric functions the following angle. 79) cot  =  3 , sin  > 0 8 x2 + y2 = r2 ( 3)2 + 82 = r2 3 + 64 = r2 67 = r2 67 = r 8  3

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