Inverse trig functions
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Inverse Trig Functions. Section 4.7 . Inverse Sine, Cosine, Tangent Functions. 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.

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Inverse Trig Functions

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Inverse trig functions

Inverse Trig Functions

Section 4.7


Inverse sine cosine tangent functions

Inverse Sine, Cosine, Tangent Functions

and it’s inverse


Inverse trig functions

y = sin x

y = arcsin x


Inverse trig functions

EXAMPLES

OR


Inverse trig functions

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range


Inverse trig functions

y = cos x

y = arccos x


Inverse trig functions

EXAMPLES

OR


Inverse trig functions

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range


Inverse trig functions

y = tan x

y = arctan x


Inverse trig functions

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range


Inverse trig functions

Let’s talk DOMAIN and RANGE…


Inverse trig functions

Let’s talk DOMAIN and RANGE…


Inverse trig functions

Let’s talk DOMAIN and RANGE…


Inverse trig functions

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


Inverse trig functions

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


Inverse trig functions

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


Inverse trig functions

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


Inverse trig functions

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


Inverse trig functions

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


Inverse trig functions

State the DOMAIN and RANGE the composite function


Inverse trig functions

Angle whose tan is x =


Inverse trig functions

#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.


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