# How do you calculate #sin(tan^-1(3/4))#?

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To calculate ( \sin(\tan^{-1}(3/4)) ), you can use the properties of trigonometric functions and the definition of the inverse tangent function.

Let ( \theta = \tan^{-1}(3/4) ). This means that ( \tan(\theta) = \frac{3}{4} ).

Using the definition of tangent, we can construct a right triangle with opposite side 3 and adjacent side 4. Then, using the Pythagorean theorem, we find that the hypotenuse is ( \sqrt{3^2 + 4^2} = 5 ).

So, in the right triangle, we have:

[ \sin(\theta) = \frac{\text{opposite}}{\text{hypotenuse}} = \frac{3}{5} ]

Therefore, ( \sin(\tan^{-1}(3/4)) = \frac{3}{5} ).

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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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