February 25, 2015
(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.
February 25, 2015
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
1. Draw the graph of a function.
2. Draw the graph of a function that is one-to-one.
3. Draw the graph of a function that isn't one-to-one.
February 25, 2015
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
y = sin x
y = sin x
resticted domain:
range:
y = sin-1 x
y = arcsin x
y = sin-1 x
February 25, 2015
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
y = cos x
y = cos x
resticted domain:
range:
y = cos-1 x
y = arccos x
y = cos-1 x
February 25, 2015
y = tan x
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
y = tan x
resticted domain:
range:
y = tan-1 x
y = arctan x
y = tan-1 x
February 25, 2015
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
Evaluate.
1. sin-1(
1
2
)
4. cos-1( √3 )
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 )
February 25, 2015
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
February 25, 2015
4. tan-1 cos ( π )
3. sin (tan-1 1)
5. sin (2 cos-1 ( √3 ) )
2
6. cos (cos (
-1
7π
4
))
February 25, 2015
Obj: To learn about the inverse sine, inverse cosine, and
inverse tangent functions.
HW:
(Reg): (4.7) Pg.385: 1-12