Identities with Inverse Trig Functions
[Pages:44]Identities with Inverse Trig Functions
Jeff Hicks Apr. 17, 2019
UC Berkeley
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 1 / 24
Summary
? Review: "Inverse" trig functions. ? Identies: Compositions of sin() and sin-1(y ). ? Example: Inverting functions with terms from trig ? Trig Identities: Right angle Identities ? Trig Identities: Even and Oddness
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 2 / 24
Review: Inverse Trig Functions
Review: Inverse Trig Functions
Definitions with a bit more meaning
Definition The function arcsine, which is written as sin-1(y )
? inputs a number y between -1 and 1,
?
outputs
the
angle
-
2
2
whose
vertical-coordinate
on
the
unit
circle is y .
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 3 / 24
Review: Inverse Trig Functions
Definitions with a bit more meaning
Definition The function arcsine, which is written as sin-1(y )
? inputs a number y between -1 and 1,
?
outputs
the
angle
-
2
2
whose
vertical-coordinate
on
the
unit
circle is y .
Definition The function arccosine, which is written as cos-1(x)
? inputs a number x between 0 and 1, ? outputs the angle 0 whose horizontal coordinate on the unit
circle is x.
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 3 / 24
Review: Inverse Trig Functions
Definition The function arctangent, which is written as tan-1(y )
? inputs a number m between - and , ? outputs the angle which represents a line of slope m.
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 4 / 24
Review: Inverse Trig Functions
What do they look like?
sin-1(y ) 1
cos-1 (x ) 2
-1 0 -1
y
1
1
tan-1(m) 1
-1 0
x 1
-5 -4 -3 -2 -1 0 -1
m
1
2
3
4
5
Jeff Hicks (UC Berkeley)
Identities with Inverse Trig Functions
Apr. 17, 2019 5 / 24
Cancelling out two functions
................
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