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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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slide3

y = sin x

y = arcsin x

slide5

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

slide6

y = cos x

y = arccos x

slide8

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

slide9

y = tan x

y = arctan x

slide10

EXAMPLES

Q: How do we explain the inconsistency??

A: It’s a matter of Domain and Range

slide14

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

slide15

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

slide16

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

slide18

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

slide19

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

slide22

#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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