Vectors and Components - Trig
Interact with the app below to discover and apply the formulas to find the components, the magnitude and the angle of a vector.
A note below the app explains how to find the correct value of using a calculator.
The Inverse Tangent Function
The angle that a vector v forms with the positive x-axis describes its direction in a two-dimensional Cartesian coordinate system.
We know that .
If we use the key of our calculator, we always obtain a value for in the interval or because that is the main interval in which the tangent function is invertible.
In the app above, drag point at , and assume that you know only the x- and y-components of the vector.
Applying the formula, you get , and using the key of your calculator you get or , that are not the angle of that you see in the app.
Because of the constraints on the result explained above, you need to adjust the calculator result for the quadrant, and precisely:
- If v is in the first quadrant , the value of is correct as is
- If v is in the second or third quadrant , add (or radians) to ensure in the 2nd or 3rd quadrant
- If v is in the 4th quadrant , add (or radians) to ensure is in the 4th quadrant.
Ready, Set, Practice!
A vector has magnitude units and its direction is . Find the horizontal and vertical components of the vector.
The horizontal component of a vector is units and its vertical component is units. Find the magnitude and the direction angle of the vector.