January 29, 2016
(4.7) Inverse Trigonometric Functions
Objective: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
Why: Inverse trig functions can be used to solve trigonometric
equations.
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
1. Describe the graph of a function.
2. Describe the graph of a function that has an inverse that is a
function.
3. What are some functions that are NOT one-to-one?
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
http://tube.geogebra.org/material/simple/id/222789
y = sin x
http://tube.geogebra.org/material/simple/id/332543
y = sin x
resticted domain:
range:
y = sin-1 x
y = arcsin x
y = sin-1 x
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
y = cos x
http://tube.geogebra.org/material/simple/id/222799
http://tube.geogebra.org/material/simple/id/1469867
y = cos x
resticted domain:
range:
y = cos-1 x
y = arccos x
y = cos-1 x
January 29, 2016
y = tan x
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
http://tube.geogebra.org/material/simple/id/222809
http://tube.geogebra.org/material/simple/id/336649
y = tan x
resticted domain:
range:
y = tan-1 x
y = arctan x
y = tan-1 x
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
Evaluate.
1. sin-1(
1
2
)
4. cos ( √3 )
-1
2
7. tan-1 ( 0 )
2. sin-1(- √2 )
3. sin-1( 1 )
5. cos ( -1 )
6. cos-1( -
2
-1
8. tan-1 ( -1 )
1
2
)
9. tan-1 (- √3 )
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
Evaluate.
1. cos-1 (cos 5π )
6
1. sin-1 (sin 5π )
3
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
Evaluate.
cos (tan-1 x)
January 29, 2016
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
HW:
(HR): (4.7) Pg.385: 1-12, 23-32, 47, 49