How do you find the limit of inverse trig functions?
The foundation lies in their definitions and the characteristics of the sine, cosine, and tangent graphs (I'll assume you are familiar with their graphs in the following).
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To find the limit of inverse trig functions, apply the following rules:

For inverse sine and cosine functions, use the fact that their range is limited to ([1, 1]). So as the input approaches (1) or (1), the output approaches the corresponding angle (\frac{\pi}{2}) or (\frac{\pi}{2}) respectively.

For inverse tangent function, as the input approaches (\pm\infty), the output approaches (\pm\frac{\pi}{2}).

For other inverse trig functions, you can use the properties of limits and algebraic manipulations to find the limit.
Remember to verify your results with the appropriate trigonometric identities and properties.
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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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