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Pre-AP PreCalculus
Notes 4.7 Inverse Trigonometric Functions
Recall that for a function to have an inverse function, it must be one-to-one – that is, it must pass
the Horizontal and Vertical Line Tests.
Would the trigonometry functions have inverses over their entire domain  ,   ?
y = sin x
y = cos x
y = tan x
What if we restricted their domains?
y = sin x
y = arcsin x
(inverse sine)
Domain_________________
Domain___________________
Range__________________
Range____________________
y = cos x
y = arcos x
Domain_________________
Domain____________________
Range__________________
Range_____________________
y = tan x
y = arctan x (inverse tangent)
Domain__________________
Domain_________________
Range__________________
Range__________________
Rules:
y= arcsin x if sin y= x
y= arcos x if cos y= x
y= arctan x if tan y= x
(inverse cosine)
If possible, find the exact value in radians (no decimals). Use the restricted domain.
Remember…the restricted domain for sine is ___________
The restricted domain for cosine is ____________
The restricted domain for tangent is ____________
1 
1

2
1) arcsin (-1)

4) arcsin  

1
2) sin 
3

2 
5) arccos
3) sin ( 3)
3
2
6) tan-1(-1)
For #7-12, find all exact radian values from [0,2 )
7) arctan (1)
1
10) cos ( 1)
1
 3

 3 
9) tan-1(0)
8) tan 

11) arcsin  

2

2 
12) arcos (0)
Calculators and Inverse Trigonometric Functions
Use a calculator to approximate all values from [0,2 ) (if possible).
13) arcsin ( .5)
14) arctan (-8.45)
15) sin-1(0.2447)
17) arctan 4.84
16) arcos 2
19) sin-1(-1.1)
18) arcos (-0.349)
If possible, find the exact value. Use the restricted domain.
20) tan[arctan(-14)]
21) cos[arcos(0.54)]


22) arcsin  sin

5 

3 
 2 

 3 
24) sin arc cos 


 3 

 4 
23) cos arctan  



25) arccos  cos
3 

2 
Practice Problems: pg 349 #1-15odd, 25-33 odd, 43, 45, 49-53 odd (assume restricted domain unless
they say otherwise).