# Simulation - Math

## Trigonometry - Sin and Cos

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Drag on the triangle to change its orientation.
Use the sliders to change the angle and the length.
The "Switch Angle" shows how to use the other angle to perform the calculation.

## Vector Components

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Drag the head of the arrow to see how its components change.

## Vector Decomposition (from angle and magnitude)

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Drag the head of the arrow to see how its components change.
Click "Switch View" to see different way to visualize the decomposition.

## Vector Addition

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Drag vectors out of the box, drag back to remove.
The individual vectors can be changed by dragging.
The red arrow is the sum of all the vectors.

#### Activity

Drag to line up (tail of one arrow on the head of another) all the blue arrows to see if they always combine to give the red arrow.
Line them up in a different order to see if they still produce the same total (red) vector.
Write out each vector in component form (i.e. with $\hat i$ and $\hat j$) and add them up algebraically to see if it gives the same result.