inverses of trigonometric functions. the sine function graph domain: range: all reals -1≤y≤1 the...
TRANSCRIPT
Inverses of Trigonometric Functions
The Sine Function Graph
Domain:
Range:All Reals
-1≤y≤1
The Sine graph is a function (one output for each input).
Let’s find the inverse of this graph.
siny x
The Inverse Sine RELATION Graph
Domain:
Range:-1≤y≤1
All Reals
1siny x
The Inverse Sine graph is NOT a function (multiple outputs for each input).
If the range of this graph is restricted, it will become a
function.
This red portion is a function. The red
portion will be known as the inverse sine
FUNCTION.
The Inverse Sine FUNCTION Graph
Domain:
Range:-1≤y≤1
1siny x
With the restriction on the range, the inverse sine function has one output for each input.
2 2x
Every output of the inverse sine function above is known as a principal value of the
inverse of sine.
The Cosine Function Graph
Domain:
Range:All Reals
-1≤y≤1
The Cosine graph is a function (one output for each
input).
Let’s find the inverse of this graph.
cosy x
The Inverse Cosine RELATION Graph
Domain:
Range:-1≤y≤1
All Reals
1cosy x
The Inverse Cosine graph is NOT a function (multiple outputs for each input).
If the range of this graph is restricted, it will become a
function.
This red portion is a function. The red
portion will be known as the inverse cosine
FUNCTION.
The Inverse Cosine FUNCTION Graph
Domain:
Range:-1≤y≤1
1cosy x
With the restriction on the range, the inverse cosine function has one output
for each input.
0 x
Every output of the inverse cosine function above is known as a principal value of the
inverse of cosine.
The Tangent Function Graph
Domain:
Range:
All Reals
The Tangent graph is a function (one output for each
input).
Let’s find the inverse of this graph.
tany x
3 32 2 2 2
All Reals except
..., , , , ,...
The Inverse Tangent RELATION Graph
Domain:
Range:All Reals
1tany x
The Inverse Tangent graph is NOT a function (multiple outputs for each input).
If the range of this graph is restricted, it will become a
function.
This red portion is a function. The red portion will be known as the inverse tangent FUNCTION.
3 32 2 2 2
All Reals except
..., , , , ,...
The Inverse Tangent FUNCTION Graph
Domain:
Range:All Reals
1cosy x
With the restriction on the range, the inverse cosine function has one output
for each input.
2 2x
Every output of the inverse tangent function above is known as a principal value of the
inverse of tangent.