# What is #cos (arcsin (5/13))#?

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First, see

That is represented by this triangle:

Now that we have the triangle that

Use the Pythagorean Theorem to determine that the adjacent side's length is

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To find cos(arcsin(5/13)), we first use the identity arcsin(sin(x)) = x for -π/2 ≤ x ≤ π/2. Therefore, arcsin(5/13) = θ, where sin(θ) = 5/13.

Using the Pythagorean identity sin^2(θ) + cos^2(θ) = 1, we can find cos(θ). Since sin(θ) = 5/13, sin^2(θ) = (5/13)^2 = 25/169.

Substituting sin^2(θ) into the Pythagorean identity, we get:

cos^2(θ) = 1 - sin^2(θ) = 1 - 25/169 = 144/169.

Taking the square root of both sides, we find:

cos(θ) = ±√(144/169) = ±12/13.

Since θ is in the first or second quadrant (0 ≤ θ ≤ π/2), cos(θ) is positive. Therefore, cos(θ) = 12/13.

So, cos(arcsin(5/13)) = 12/13.

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When evaluating a one-sided 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 one-sided 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 one-sided 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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