Trigonometric Ratios - Mathematics and Statistics for the Environment - page 101

6 Trigonometric Ratios
sin A = a / c cos A = b / c tan A = a / b
We owe a lot to the Indians, who taught us how to count, without which no worthwhile scientific dis-
covery could have been made.
—Albert Einstein
Trigonometry is the branch of mathematics that is used to compute unknown angles and sides of
triangles. The word trigonometry is derived from the Greek words for triangle and measurement.
Trigonometry is based on the principles of geometry. Many problems require the use of geometry and
trigonometry.
— Smith and Peterson (2007)
6.1 TRIGONOMETRIC FUNCTIONS AND
THE ENVIRONMENTAL PRACTITIONER
Typically, environmental practitioners are called upon to make calculations involving the use of
various trigonometric functions. Consider slings, for example; they are commonly used with cranes,
derricks, and hoists to lift a load and move it to the desired location. For the environmental profes-
sional responsible for safety and health, knowledge of the properties and limitations of the sling,
the type and condition of material being lifted, the weight and shape of the object being lifted, the
angle of the sling to the load being lifted, and the environment in which the lift is to be made are all
important considerations to be evaluated before the safe transfer of material can take place. Later,
we put many of the following principles to work in determining sling load and working load on a
ramp (inclined plane)—that is, to solve force-type problems. For now, we discuss the basic trigono-
metric functions used to make such calculations.
6.2 TRIGONOMETRIC RATIOS OR FUNCTIONS
In trigonometry, all computations are based on certain ratios (i.e., trigonometric functions). The
trigonometric ratios or functions are sine, cosine, tangent, cotangent, secant, and cosecant. It is
important to understand the definition of the ratios given in Table 6.1 and defined in terms of the
lines shown in Figure 6.1.
Note: In a right triangle, the side opposite the right angle is the longest side. This side is called the
hypotenuse . The other two sides are the legs .
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