3 /2 2 5 /2

2.5 00

2.0 00

1.5 00

1.0 00

0.5 00

-/2

0.0 00 -0.5 00

-1.0 00

-1.5 00

-2.0 00

-2.5 00

2.500 2.000 1.500 1.000 0.500 0.000

-/2

-0.500 -1.000 -1.500 -2.000 -2.500 2

y = sin x

y=csc x

/2

3/2

2

5/2

y = cos x

y=sec x

/2

3/2

2

5/2

y = tan x

y=cot x

In order for sec, csc, and cot to have inverse functions, we need to restrict their domains to intervals that are one-to-one. That is, the graphs must be strictly increasing or strictly decreasing for a certain interval. Can you find any intervals that can pass the Horizontal Line Test?

1

0

-/2

-1

/2

3/2

2

5/2

-2

Properties of Inverse Trig Functions ARCSIN y = sin-1 x means x = sin y Domain (input): {x|-1x1} Range (output): {y| -/2 y /2}

ARCCOS y = cos-1 x means x = cos y Domain (input): {x|-1x1} Range (output):{y|0 y }

ARCTAN y = tan-1 x means x = tan y Domain (input): {all real numbers} Range (output): {y| -/2 y /2}

ARCCSC y = csc-1 x means x = csc y Domain (input): {x|x -1 or x1 } Range (output):{y| -/2 y /2 and y 0

Since |cos y| 1, then |1/cosy| 1

ARCSEC

Because 1/(sin 0) is undefined.

y = sec-1 x means x = sec y Domain (input): {x|x -1 or x1 } Range (output):{y|0 y and y /2}

Since |cos y| 1, then |1/cosy| 1

ARCCOT

Because 1/(cos /2) is undefined.

y = cot-1 x means x = cot y

Domain (input): {all real numbers}

Range (output):{y|0 ................
................

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