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TRIGONOMETRY 1/2
Trigonometry, which has its roots in ancient Greece, was developed to obtain the measurements of triangles. Of course, this is not the only application or even the most important use of trigonometry which can also be developed as functions of real numbers. The effects of trigonometry are so widespread. Surveyors, construction workers, navigators, as well as many scientists all use trigonometry in their professions. Ah, the power of math.
1. RADIANSAs you have already learned, two ways to measure an angle are degrees(°) and radians. An angle measuring 1 radian intercepts an arc equal in length to the radius of the circle. As shown below, 1 rad is approximately 57°. Also, 2 p radians = 360°.
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2. RIGHT TRIANGLE TRIGONOMETRYThe classic definitions of the six trigonometric functions sine (sin), cosine (cos), tangent (tan), cosecant (csc), secant (sec), and cotangent (cot) and are based on the six possible ratios of the sides of a right triangle. With respect to the angle a in the triangle shown, we see that a= opposite side (opp), b= adjacent side (adj), and c= hypotenuse (hyp). Then we can define the functions:
Sine, cosine and tangent are generally considered the three principle trigonometric functions. From the definitions, it is easy to see why cosecant, secant and cotangent are reciprocals, respectively, of these three main functions. |
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From the sketch
and definitions, other relations can be seen:  
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