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.

All Students Take Calculus

S A Sin All

T C Tan Cos

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Identify the quadrant or quadrants for the angles satisfying the following conditions.

19)sin >0, cos <0

I, II

I, II II, III

21)sec <0, csc <0

II, III

II, III III, IV

23)Sin <0, cos >0

III, IV

III, IV I, IV

Identify the quadrant or quadrants for the angles satisfying the following conditions.

25)tan <0, cot <0

II, IV

II, IV II, IV

27) sin > 0

I, II

29) tan > 0

I, III

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

– | + | – | – | + | – |

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

– | – | + | + | – | – |

1.5 Using the Definitions of the Trigonometric Functions

OBJ: • Find the other trigonometric functions, given one of them and quadrant information

Find the following trigonometric function, given a trigonometric function & quadrant information

EX: cos = - 3 , in Q II; Find sin 4

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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

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Find the following trigonometric function, given a trigonometric function & quadrant information

61) sin = 2 , in Q II; Find cos 3

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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

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Find the following trigonometric function, given a trigonometric function & quadrant information

63) cot = -1, in Q IV; Find csc 2

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Find the following trigonometric function, given a trigonometric function & quadrant information63) 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

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Find the following trigonometric function, given a trigonometric function & quadrant information

65) tan = 7, in Q III; Find sec 3

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Find the following trigonometric function, given a trigonometric function & quadrant information

65) tan = 7, in Q III; Find sec 3x2 + y2 = r2

(-3)2 + (- 7)2 = r2

9 + 7 = r2 -316 = r2

4 = r - 7

sec = 4 -3

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Find all the other trigonometric functions the following angle.

69) cos = - 3 , in Q III

5

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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

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Find all the other trigonometric functions the following angle.73) csc = 2 , in Q II

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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

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Find all the other trigonometric functions the following angle.77) sin = -5 , cos > 0

6

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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

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Find all the other trigonometric functions the following angle.79) cot = 3 , sin > 0

8

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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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