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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. - PowerPoint PPT Presentation
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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
y
x
5
5
-5-5
y
x
5
5
-5-5
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
y
x
5
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
y
x
5
5
-5-5
Find the following trigonometric function, given a trigonometric function & quadrant information
61) sin = 2 , in Q II; Find cos 3
y
x
5
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
y
x
5
5
-5-5
Find the following trigonometric function, given a trigonometric function & quadrant information
63) cot = -1, in Q IV; Find csc 2
y
x
5
5
-5-5
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
y
x
5
5
-5-5
Find the following trigonometric function, given a trigonometric function & quadrant information
65) tan = 7, in Q III; Find sec 3
y
x
5
5
-5-5
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
y
x
5
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-5-5
Find all the other trigonometric functions the following angle.
69) cos = - 3 , in Q III
5
y
x
5
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
y
x
5
5
-5-5
Find all the other trigonometric functions the following angle.73) csc = 2 , in Q II
y
x
5
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
y
x
5
5
-5-5
Find all the other trigonometric functions the following angle.77) sin = -5 , cos > 0
6
y
x
5
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
y
x
5
5
-5-5
Find all the other trigonometric functions the following angle.79) cot = 3 , sin > 0
8
y
x
5
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
y
x
5
5
-5-5
