inverses of trigonometric functions. the sine function graph domain: range: all reals -1≤y≤1 the...

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Inverses of Trigonometric Functions

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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)

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)

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)

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)

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)

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)

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)

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)

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)

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)

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.