Transcript Advanced Precalculus Notes 6.1 The Inverse Sine, Cosine

Advanced Precalculus Notes 6.1 The Inverse
Sine, Cosine, and Tangent Functions
y = sin x and
y = sin-1x
graphed over the interval [-2 π , 2π ]
y  sin 1 x
y  sin x
Dom ain:   x  
Dom ain: 1  x  1
Range: 1  y  1
Range: 

2
 y

2
Find the exact value of each:
1
a) sin 1
1
b) sin (  )
2
1
Use a calculator to find an approximate value of each:
1
a ) sin ( )
3
1
1
b) sin (  )
4
1
y  cos x
Dom ain:   x  
Range: 1  y  1
y  cos1 x
Dom ain: 1  x  1
Range: 0  y  
Find the exact value of each:
1
a) cos 1
1
b) cos (  )
2
1
Use a calculator to find an approximate value of each:
1 1
a) cos ( )
3
1
b) cos (  )
4
1
y  tan x
Dom ain: x 

 n
2
Range:   y  
y  tan1 x
Dom ain:   x  
Range: 

2
 y

2
Find the exact value of each:
b) tan1 ( 3)
1
a) tan 1
Find the exact value of each:
1
a) cos [cos(

12
)]
1
b) cos[cos (0.4)]
1
1
a) Does : tan[tan ( )]  
2
2
1
1
b) Does: cos[cos (2)]  2 ?
Assignment:
page 457:
1 – 12, 13 - 55 odds, 57,
64 a, b