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Inverse Trig Functions

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Inverse Trig Functions

Section 4.7

and it’s inverse

y = sin x

y = arcsin x

EXAMPLES

OR

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

y = cos x

y = arccos x

EXAMPLES

OR

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

y = tan x

y = arctan x

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

Let’s talk DOMAIN and RANGE…

Let’s talk DOMAIN and RANGE…

Let’s talk DOMAIN and RANGE…

Now some examples…Evaluate w/out Calc

Find the cosine of the angle whose sine is ½

Start with innermost expression

Work your way out

Evaluate

Now some examples…Evaluate w/out Calc

Find the angle whose sine is the cosine of

Start with innermost expression

Work your way out

Evaluate

Now some examples…Evaluate w/out Calc

Find the angle whose cos is the tangent of

Start with innermost expression

Work your way out

Evaluate

Example: #41 & #42*, P. 422

State the DOMAIN and RANGE the composite function

Decide the domain of innermost function

This is your DOMAIN

Find RANGE of innermost function

This is the DOMAIN of the outer function

Determine the RANGE based on “new” DOMAIN

State the DOMAIN and RANGE the composite function

Decide the domain of innermost function

This is your DOMAIN

Find RANGE of innermost function

This is the DOMAIN of the outer function

Determine the RANGE based on “new” DOMAIN

State the DOMAIN and RANGE the composite function

Angle whose tan is x =

#25, p. 433: A boat is due east of the shoreline running north/south. The bearings of the boat from two points on the shore that are 550’ apart from each other are 100 and 110 degrees. How far is the boat from the shore?

x

Consider two of the triangles formed in the diagram.