2
3.1 Inverse Trig Functions
Review of basic inverses:
Def:
Does every function have an inverse?
Graphical properties:
Domain/Range Properties
Def of y = Arcsin x = Sin-1 x
[pic]
Domain: [-1, 1] Range: [-π/2, π/2]
Def of y = Arccos x = Cos-1 x
[pic]
Domain: [-1, 1] Range: [0, π]
Def of y = Arctan x = Tan-1 x
[pic]
Domain: (-∞, ∞) Range: (-π/2, π/2)
Note: Angles are ALWAYS in RADIANS!!!!!!!
Examples: Evaluate the following EXACTLY:
a) Cos-1(1/2)
b) Arcsin(1/2)
c) Tan-1((3)
d) Cos-1(-(3/2)
e) Sin-1(-(3/2)
f) Sin-1((3/2)
g) Tan-1(-1)
h) Arccos(-(2/2)
i) Tan-1(-(3/3)
j) Sin-1((3)
k) cos(π/3)
l) Cos-1(π/3)
Determine if the following statements are True T or False F. Explain WHY.
To do these we MUST KNOW the domain and range of the trig functions
| |Domain |Range |
|[pic] | | |
|[pic] | | |
|[pic] | | |
[pic] only if x in the domain of composition i.e in the domain of f-1 and range of f
[pic] only if x in the domain of composition i.e in the domain of f and range of f-1
a) Arcsin(sin(π/3))= π/3 True / False
because
b) Arcsin(sin(7π/6))= 7π/6 True / False
because
c) cos-1(cos(2π/3))= 2π/3 True / False
because
d) cos-1(cos(-π/3))= -π/3 True / False
because
e) cos(cos-1(-1/2))=-1/2 True / False
because
f) sin(sin-1(π))=π True / False
because
g) tan-1(tan 5π/3) = 5π/3 True / False
because
Calculator problems: You must be in Radian mode!! Always give answer accurate to 4 decimals unless specified otherwise.
cos-1(-1/2)
sin-1(1/5)
cos-1(π/2)
tan-1(-8.2)
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