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3 years ago

What is 0.464646... as a fraction

Mathematics

1 answer:

rewona [7]3 years ago

7 0

This is what I get

You have to place the decimal numbers over the power of 10.since its 6 places to the right will be 10^6(1000000).

464646/1000000

Now cancel common factors by factoring out 2.

232323/500000=0.464646

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Step-by-step explanation:

For this case we need to proof the following identity:

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We need to begin with the definition of tangent:

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$tan(x-y) = \frac{sin(x-y)}{cos(x-y)}$ (1)

We have the following identities useful for this case:

$sin(a-b) = sin(a) cos(b) - sin(b) cos(a)$

$cos(a-b) = cos(a) cos(b) + sin (a) sin(b)$

If we apply the identities into our equation (1) we got:

$tan(x-y) = \frac{sin(x) cos(y) - sin(y) cos(x)}{sin(x) sin(y) + cos(x) cos(y)}$ (2)

Now we can divide the numerator and denominato from expression (2) by $\frac{1}{cos(x) cos(y)}$ and we got this:

$tan(x-y) = \frac{\frac{sin(x) cos(y)}{cos(x) cos(y)} - \frac{sin(y) cos(x)}{cos(x) cos(y)}}{\frac{sin(x) sin(y)}{cos(x) cos(y)} +\frac{cos(x) cos(y)}{cos(x) cos(y)}}$

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