To find the component in the East/West direction (or X): This means the side opposite 60º is parallel to the x-axis (East/West), and the adjacent side is parallel to the y-axis (North/South). The vector drawn on the right is 60º clockwise from the y-axis (which is north when using the convention for navigation).

To convert magnitude and direction to the axial components, use trig equations. In all cases, the hypotenuse will be the magnitude of the vector. First, identify the angle to an axis of interest and then apply the appropriate trig function. This spatial relationship means that we use trig functions to find the axial components of vectors if we know the magnitude and direction. Since the axes that define the direction of a vector are perpendicular to each other, a right triangle also describes a vector relative to the axes. Tangent( θ) = tan( θ ) = H / W = opposite / adjacent = sin( θ ) / cos( θ )Ĭalculating Vector Components from Magnitude & Direction In addition, there is a function that involves both the sin and cos functions. The ratio W/L is the cosine of θ :Ĭosine( θ ) = cos( θ ) = W / L = adjacent / hypotenuse The base of the triangle, W, is also significant in other physical phenomena. Sine( θ ) = sin( θ ) = H / L = opposite / hypotenuse When a quantity keeps appearing in a calculation’s final form, mathematicians, scientists, and engineers pay attention. Both H/L and θ indicate the pitch or slope of the ramp. Both triangles have the same angle of inclination, θ. This means that its hypotenuse is only L. Insert a similar right triangle a vertical side length of H. For instance, consider the large right triangle with hypotenuse 2L and vertical side length 2H. When analyzing variables associated with right triangles, the ratio, H/L, keeps popping up again and again.

Special right triangles calculator