inverses of trigonometric functions. the sine function graph domain: range: all reals -1≤y≤1 the...
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![Page 1: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/1.jpg)
Inverses of Trigonometric Functions
![Page 2: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/2.jpg)
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
![Page 3: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/3.jpg)
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.
![Page 4: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/4.jpg)
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.
![Page 5: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/5.jpg)
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
![Page 6: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/6.jpg)
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.
![Page 7: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/7.jpg)
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.
![Page 8: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/8.jpg)
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
..., , , , ,...
![Page 9: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/9.jpg)
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
..., , , , ,...
![Page 10: 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)](https://reader036.vdocuments.us/reader036/viewer/2022082411/56649d995503460f94a83c8b/html5/thumbnails/10.jpg)
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.