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Featured 2 months ago

Compute vector C:

Compute the dot-product of vectors A and C:

There is another form for the equation of the dot-product that contains the angle between the two vectors:

Compute the magnitude of vector A:

Compute the magnitude of vector C:

Featured 2 months ago

(see below)

Based on the Pythagorean Theorem, we know that

#color(white)("XXX")a^2+b^2=c^2

Featured 2 months ago

Another way, without calculating

Consider a right triangle with an angle

Thus

Note that this same reasoning shows that in general,

Featured 2 months ago

Given expression

Let

So

**Inserting**

Featured 2 months ago

Set your compass to a radius of 6, put the center point at

Multiply both sides of the equation by r:

Substitute

The standard form of this type of equation (a circle) is:

To put the equation in this form, we need to complete the square for both the x and y terms. The y term is easy, we merely subtract

To complete the square for the x terms, we add

We can use the pattern,

Substitute 6 for h into the equation of the circle:

We know that the first three terms are a perfect square with h = 6:

This is a circle with a radius of 6 and a center point

Featured 1 month ago

Please see the explanation.

Here is the graph:

This looks like a cosine function that has been multiplied by an amplitude and phase shift to the right:

My graphing tool allows me to obtain values of points and I can tell you that

This fits the trigonometric identity:

where

This happens at

The graphing tool confirms that the x coordinates are shift by

Substitute

The left side becomes x by definition:

Make the

Use the inverse cosine on both sides:

Solve for

To confirm that this is truly an inverse, verify that

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