How do you evaluate #cos^1(sin(pi/6))# without a calculator?
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To evaluate ( \cos^{1}(\sin(\frac{\pi}{6})) ) without a calculator:

First, note that ( \sin(\frac{\pi}{6}) = \sin(\frac{\pi}{6}) = \frac{1}{2} ).

Recall that the cosine function is positive in the first and fourth quadrants and negative in the second and third quadrants.

Since ( \sin(\frac{\pi}{6}) = \frac{1}{2} ), we're dealing with the fourth quadrant where cosine is positive.

In the fourth quadrant, ( \cos^{1}(x) ) is the angle whose cosine is ( x ) and lies in the range ( [0, \pi] ).

The angle whose cosine is ( \frac{1}{2} ) in the fourth quadrant is ( \frac{2\pi}{3} ).
So, ( \cos^{1}(\sin(\frac{\pi}{6})) = \frac{2\pi}{3} ).
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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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