sin
opposite
hypotenuse
a
c
cos
adjacent
hypotenuse
b
c
tan
opposite
adjacent
a
b
VECTORS: RESULTANTS AND COMPONENTS
Vectors
CP-02
Page 12
Rev. 0
Figure 13 Right Triangle
As an exercise, the student should graphically find the easterly and northerly components of a
13 mile displacement at 22.6 north of east. The correct answer is 5 miles east and 12 miles
o
north.
Trigonometry may also be used to determine vector components. Before explaining this method,
it may be helpful to review the fundamental trigonometric functions. Recall that trigonometry is
a branch of mathematics that deals with the relationships between angles and the length of the sides
of triangles. The relationship between an acute angle of a right triangle, shown in Figure 13, and
its sides is given by three ratios.
(2-1)
(2-2)
(2-3)
Before attempting to calculate vector components, first make a rough sketch that shows the
approximate location of the resultant vector in an x-y coordinate system. It is helpful to form a
visual picture before selecting the correct trigonometric function to be used. Consider the example
of Figure 12, that was used previously. This time the component vectors will be calculated.
