How do you graph inverse trigonometric functions?
Since the graphs of
(Caution: Their domains must be restricted to an appropriate interval so that their inverses exist.)
Let us sketch the graph of
The graph of
By reflecting the graph above about the line
The curve in purple is the graph of
The graphs of other inverse trigonometric functions can be obtained similarly.
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To graph inverse trigonometric functions, you typically follow these steps:

Understand the Function: Have a clear understanding of the inverse trigonometric function you're dealing with. Common ones include arcsin (inverse sine), arccos (inverse cosine), and arctan (inverse tangent).

Determine the Domain and Range: Each inverse trigonometric function has a restricted domain and range to ensure it is onetoone and has an inverse. For example, arcsin has a domain of [1, 1] and a range of [π/2, π/2], arccos has a domain of [1, 1] and a range of [0, π], and arctan has a domain of all real numbers and a range of [π/2, π/2].

Plot Key Points: Identify key points on the graph based on the function's domain and range. These points typically include the endpoints of the domain and the corresponding values of the function.

Draw the Graph: Connect the key points with a smooth curve, maintaining the characteristics of the function, such as concavity and direction.

Label Axes and Units: Label the xaxis and yaxis appropriately, indicating the units if necessary.

Add Additional Information: Depending on the context or specific requirements, you may need to add additional information to the graph, such as asymptotes or important intervals.

Check Symmetry: Inverse trigonometric functions often exhibit symmetry properties. For example, the arcsin function is symmetric about the line y = x, while arccos is symmetric about the line y = π  x.
By following these steps, you can accurately graph inverse trigonometric functions, providing visual representations of their behavior and characteristics.
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When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
When evaluating a onesided limit, you need to be careful when a quantity is approaching zero since its sign is different depending on which way it is approaching zero from. Let us look at some examples.
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