A bit more practice in Section 4.7b. Analysis of the Inverse Sine Function. 1. –1. D:. R:. Continuous. Increasing. Symmetry: Origin (odd . func. .). Bounded. Abs. Max. of at . x. = 1. Abs. Min. of at . ID: 486331
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Inverse Trigonometric Functions
A bit more practice in Section 4.7b
Slide2Analysis of the Inverse Sine Function
1
–1
D:
R:
Continuous
Increasing
Symmetry: Origin (odd
func
.)
Bounded
Abs. Max. of at
x
= 1
Abs. Min. of at
x
= –1
No Asymptotes
No End Behavior (bounded domain)
Slide3Analysis of the Inverse Cosine Function
D:
R:
Continuous
Decreasing
Symmetry: About the point
Bounded
Abs. Max. of at
x
= –1
Abs. Min. of at
x
= 1
No Asymptotes
No End Behavior (bounded domain)
1
–1
Slide4Analysis of the Inverse Tangent Function
D:
R:
Continuous
Increasing
Symmetry: Origin (odd
func
.)
Bounded
No Local
Extrema
Horizontal Asymptotes:
End Behavior:
Slide5Guided Practice
Use a calculator to find the approximate value. Express youranswer in both degrees and radians.
(a)
(b)
(c)
Slide6A note about composing trigonometricand inverse trigonometric functions…
The following equations are always true whenever theyare defined:
On the other hand, the following equations are only true for
x
values in the “restricted” domains of sin,
cos
, and tan:
Slide7Whiteboard Practice…
Find the exact value without a calculator.
(a)
Evaluate this inverse portion first…
(b)
(c)
Slide8Whiteboard Practice…
Find the exact value without a calculator.
(d)
(e)
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