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Mathematics

2 answers:

olga nikolaevna [1]3 years ago

3 0

As time time starts at zero, he is at home. As time goes on, he travels to a given location, which is why his distance increases. He then stays there for a while which is why the time continues to go on but his distance doesn't change. He then rides home quickly.

ss7ja [257]3 years ago

3 0

Manuel rides his bike from his house to a given location at an constant speed for a while, he then stops for a short period of time and then travels to the given location (or the grocery store for an example)

Hope this helps!!

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Write the trigonometric expression in terms of sine and cosine, and then simplify. cot()/sin()-csc()

OLEGan [10]

Answer:

First, we know that:

cot(x) = cos(x)/sin(x)

csc(x) = 1/sin(x)

I can't know for sure what is the exact equation, so I will assume two cases.

The first case is if the equation is:

$\frac{cot(x)}{sin(x)} - csc(x)$

if we replace cot(x) and csc(x) we get:

$\frac{cot(x)}{sin(x)} - csc(x) = \frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)}$

Now let's we can rewrite this as:

$\frac{cos(x)}{sin(x)} \frac{1}{sin(x)} - \frac{1}{sin(x)} =\frac{cos(x)}{sin^2(x)} - \frac{1}{sin(x)}$

$\frac{cos(x)}{sin^2(x)} - \frac{sin(x)}{sin^2(x)} = \frac{cos(x) - sin(x)}{sin^2(x)}$

We can't simplify it more.

Second case:

If the initial equation was

$\frac{cot(x)}{sin(x) - csc(x)}$

Then if we replace cot(x) and csc(x)

$\frac{cos(x)}{sin(x)}*\frac{1}{sin(x) - 1/sin(x)} = \frac{cos(x)}{sin(x)}*\frac{1}{sin^2(x)/sin(x) - 1/sin(x)}$

This is equal to:

$\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1}$

And we know that:

sin^2(x) + cos^2(x) = 1

Then:

sin^2(x) - 1 = -cos^2(x)

So we can replace that in our equation:

$\frac{cos(x)}{sin(x)}*\frac{sin(x)}{sin^2(x) - 1} = \frac{cos(x)}{sin(x)}*\frac{sin(x)}{-cos^2(x)} = -\frac{cos(x)}{cos^2(x)}*\frac{sin(x)}{sin(x)} = - \frac{1}{cos(x)}$