sin - cos
tan - cot

The most appropriate method to calculate components of forces is using trigonometrical ratios, like sin, cos, tan of an angle. The ratio for sin and cos range between 0 and 1.
sin 0 = 0 and cos 0 = 1
sin 90 = 1 and cos 90 = 0
uc-sincos.gif Tri-sin.gif
Figure 1

Look at the unit circle shown in Figure 1 (a). The sin (cos) of an angle is the relationship of the vertical and horizontal component of the given angle. Using the right angle triangle, shown in Figure 1 (b), we can calculate the sides of any rectangle triangle. The following formulas are used for the calculation of the sides:


Force vectors are in most cases shown at a given angle, they equate to the hypotenuse of the right angle triangle. We need to find the horizontal and vertical component of the force vector.

The vertical component is: Opposite = Hypotenuse × sin theta-uc.gif
The horizontal component is: Adjacent = Hypotenuse × cos theta-uc.gif

Those statements are always true if you select the angle of the force to the horizontal reference line. If the angle to the vertical is given use the supplement angle (90 - Q)

Tangent and Cotangent

If the hypotenuse is not needed or given than we can calculate the length of the vertical or horizontal or the angle using tan or cot.

Again the tan of an angle is

uc-tan.gif tri-tan.gif

An easy way to deal with sin, cos, tan and cot is shown below. Each formula consist of three figures:

Sin = Opposit over the Hypotenuse.

If you have trouble with formula transposition look at the letters in the triangle. they give you an indication how to transpose the formula.

tri-s-c-t-v.gif tri-equat1.gif

Sin & cos values for the most common angles.

Sin rule
sin : sin : sin = a : b : c
a : sin = b : sin =  c : sin

Cos rule
a² = b² + c² - 2 bc x cos
b² = c² + a² - 2 ac x cos
c² = a² + b² - 2 ab x cos

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