The definitions of the six trigonometric functions of angle
A are listed below.
For any angle congruent to angle A, the numerical value of any of these ratios will be equal to the value of that ratio for angle A. Consequently, for any given angle, these ratios have specific values that are listed in tables or can be found on calculators.
Basic Uses of Trigonometry. The definitions of the six functions and the Pythagorean Theorem provide a powerful means of finding unknown sides and angles. For any right triangle, if the measures of one side and either another side or angle are known, the measures of the other sides and angles can be determined.
For example, suppose the measure of angle A is 36° and side c measures 12 centimeters (and angle C measures 90°). To determine the measure of angle B, subtract 36 from 90 because the two non-right angles must sum to 90°. To determine sides a and b, solve the equations sin and cos , keeping in mind that sin 36° and cos 36° have number values. The results are a = 12sin 36° ≈ 7.1 cm and b = 12cos 36° ≈ 9.7 cm.
Two theorems that are based on right-triangle trigonometry—the Law of Sines and the Law of Cosines—allow us to solve for the unknown parts of any triangle, given sufficient information.
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