# How do you use the half-angle identity to find the exact value of sin (-pi/12)?

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You can use the half-angle identity for sine to find the exact value of sin(-π/12) as follows:

sin(θ/2) = ±√((1 - cos(θ)) / 2)

sin(-π/12) = sin((-π/6)/2)

sin((-π/6)/2) = ±√((1 - cos(-π/6)) / 2)

First, find the value of cos(-π/6):

cos(-π/6) = cos(π/6) = √3/2

Now, substitute cos(-π/6) into the half-angle identity:

sin(-π/12) = ±√((1 - √3/2) / 2)

To determine the sign, consider the quadrant. Since -π/12 is in the fourth quadrant where sine is negative:

sin(-π/12) = -√((1 - √3/2) / 2)

Then, simplify to find the exact value of sin(-π/12).

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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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