Graph one cycle and fill in the blanks.
1
1. y
Period = _____
sec 2 x
1
2
2
Equation of Asymptotes ___________________
Three Specific Asymptotes
______________
_______________________________________________________________________________
2. y
3cot x
6
1
Period = _____
Equation of Asymptotes ___________________
Two Specific Asymptotes
______________
_______________________________________________________________________________
3. y
Period = ____
2csc 2x 1
Equation of Asymptotes
___________________
Three Specific Asymptotes
______________
10
4. y
3
tan x
2
6
Period = _____
Equation of Asymptotes ___________________
Two Specific Asymptotes ______________
___________________________________________________________________________
Write the equation for each graph.
5.
Equation: ______________________________
6.
Equation: ________________________________
11
Evaluate.
2
7. cos
3
8. tan
10. cot
2
3
13. cos
5
5
sin
sin
cos
6
4
6
4
14. cos
3
7
cos
4
6
5
4
9. sin
5
6
12. sec3
11. csc
sin
5
3
3
7
sin
4
6
7
3
4
15.
7
1 tan tan
3
4
tan
tan
________________________________________________________________________________
If 0
in radians that make each statement true.
2 , determine the values of
3
16. cos
17. tan
18. csc
3
2
2
19. cot 2
1
3
20. sec2
4
3
21. csc2
2
12
Notes on graphing inverses of sine and cosine graphs
1st Graph y = sin x
2 nd Interchange the values in the ordered pair and sketch in
the graph below:
angle
value
angle
3rd graph y
value
Sin 1 ( x)
angle
value
_______________________________________________________________________________________________________
Part 2 ) Do the same as above but to the graph y = cosine x
1st Graph y = cos x
2 nd Interchange the values in the ordered pair and sketch in the graph below:
angle
value
angle
3rd graph y
Cos 1 ( x )
value
angle
value
13
1st
2 nd Interchange the values in the ordered pair and sketch in the graph below:
Graph y = tan x
angle
value
angle
3rd graph y
tan 1 ( x)
value
angle
value
_______________________________________________________________________________________________________
Part 2 ) Do the same as above but to the graph y = cosine x
1st Graph y = cot x
2 nd Interchange the values in the ordered pair and sketch in the graph below:
angle
value
angle
3rd graph y
Cot 1 ( x)
value
angle
value
14
INVERSE TRIG FUNCTIONS PROBLEMS NOTES
TWO GROUPS BASED ON SIMILAR RANGE
y = sin 1 x
[
y = tan 1 x
(
y = csc 1 x
[
2, 2
2
]
2, 2
)
2, 2
] , y 0
2
Sample Problems
3
5
Reference Triangles
3
ex 1 sin(arctan( )
2
cot(sin 1 (
10
))
10
sec(arc tan 3x)
Angle Problems
4
sin 1 (
3
)
2
5
arc tan(-1)
6
arcsin(tan
3
)
4
SECOND GROUP
y
cos 1 x
[0, ]
y
sec 1 x
[0, ]
y
cot 1 x
(0, )
y
2
0
15
Sample Problems
Reference Triangles
3
3
5
ex 1 sin(arccos( ) )
2
sin(cos 1 (
10
))
10
sec(arc csc 3x)
Angle Problems
4
cos 1 (
3
)
2
5
arc cot(-1)
6
arcsin(cos
3
)
4
Summary of quadrant locations for inverse functions.
16
Examples:
Find the exact values without using a calculator.
1.
sin
1
1 = ________
3.
sin
1
1
________
2
5.
tan
1
7.
Arc csc 2 = ____________
9.
sec
1
2.
4.
cos
3
= __________
2
1
1
= __________
2
A rccos
6.
csc
1
2
3
8.
sec
1
2 = ____________
10.
A rc cot
1
= _______________
3
1
= ______________
2
12.
A rcsin sin
7
6
= __________
14.
sin
3 = ________
2 = _____________
= __________
Find the exact value:
11.
sin A rccos
13.
Arc sec sec
15.
sin cos
1
3
4
= _________
16.
cos A rcsin
17.
tan sin
1
1
2
= _________
18.
sin tan 1( 1) = _____________
19.
cos cot
1
= ________
20.
cos A rcsin
21.
sin Arc cos
3
= _________
4
22.
csc cos
23.
Arccot(-1)=_______________
24.
cot
4
12
5
1
1
sin
= _______________
4
1
= _____________
2
7
= __________
5
13
2
9
= __________
= ____________
3 = ___________
17