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Featured 6 months ago

Polar coordinate

and at an angle of

Note that the angle

Featured 5 months 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

Featured 4 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 4 months ago

If

then

and

If

then

and

Plugging in the values for

If we call this value

then

and (since

Featured 1 month ago

Use the double angle formula for cosine to expand

Let

Featured 1 month ago

Here is the graph of

Step 1: Sketch the graph of

Step 2: Sketch the line

Step 3: Reflect the graph of

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