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The
graph of the tangent function
and the
cotangent function |
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The
graph of the
arc-tangent function and the arc-cotangent function |
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| The
graph of the tangent function
and the
cotangent function |
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- The
arc-tangent function
y
= tan-1x
or y
= arctan x
is the inverse of the tangent function, so that its value for any
argument is an arc (angle) whose tangent equals the given
argument. |
| That
is, y
= tan-1x
if and only if x
= tan
y.
For
example, |
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Thus, the arc-tangent
function is defined for all real arguments, and its principal
values are by
convention taken to be those strictly between -p/2
and p/2. |
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- The
arc-cotangent function
y
= cot-1x
or y
= arccot x
is the inverse of the cotangent function, so that its value for any
argument is an arc (angle) whose cotangent equals the given
argument. |
| That
is, y
= cot-1x
if and only if x
= cot
y.
For
example, |
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Thus, the arc-cotangent
function is defined for all real arguments, and its principal
values are by
convention taken to be those strictly between 0
and p. |
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| The
graph of the
arc-tangent function and the
arc-cotangent function |
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