# How do you evaluate sine, cosine, tangent of #(4pi)/3# without using a calculator?

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To evaluate sine, cosine, and tangent of (4π)/3 without using a calculator, you can refer to the unit circle.

For (4π)/3:

- The reference angle is π/3.
- In the unit circle, π/3 corresponds to the point (1/2, √3/2).

Since (4π)/3 is in the second quadrant:

- Sine is positive, so sin((4π)/3) = √3/2.
- Cosine is negative, so cos((4π)/3) = -1/2.
- Tangent is the ratio of sine to cosine, so tan((4π)/3) = (√3/2) / (-1/2) = -√3.

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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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