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Featured 4 months ago

Letting,

The Expression

Featured 4 months ago

The distance is

Change the -1 radius to +1 by adding

Find the difference between the two angles:

We can find the distance between them using the Law of Cosines where side

Featured 4 months ago

Let

So

Now

Featured 4 months ago

THe angle is 66.2Âº

The dot product betwwen 2 vectors is

If

and

The dot product is

let

so the angle

Featured 2 months ago

See below:

With a triangle with

We could run through the pythagorean theorem for the third side, but we can also remember that these two measurements are part of a 30-60-90 triangle, and so the third side is

This gives us the 6 trig ratios:

The angle of the triangle we're looking at is

Featured 1 month ago

The explanation is written with the assumption that you meant

Use the distributive property :

Substitute x for

Square both sides:

Add

Remove a factor of the 3 from the first 3 terms:

Use the middle in the right side of the pattern

Substitute the left side of the pattern into the equation:

Substitute

Divide both sides by

Write the denominators as squares:

The is standard Cartesian form of the equation of an ellipse with a center at

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