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# Trig questions. I am having trouble understanding the methods.?

Topic: What are the problem solving methods
July 16, 2019 / By Claribel
Question: I would like to know how to determine the method used to solve certain trig problems.. My instructor doesn't give me much information on the subject. Example: Use periodic function to find the value of cot 15pie/2. Evaluate the quadrantal angle csc pie. I need to know how to tell what type operation needs to be used to find the different Trig functions of an angle.. Any help?

## Best Answers: Trig questions. I am having trouble understanding the methods.?

Bea | 2 days ago
Your instructor appears to be trying to make the point that periodic functions are, periodic. So the cot(15PI/2) = cot(6PI + 3PI/2) = cot(3PI/2). Since each 2PI we add simply increments the independent variable by one full period, we can divide out and drop the even multiples, using only the remainder to find the value of the function. And, since cot = cos/sin we may also use what we know of the values for cos and sin at 3PI/2 to find the answer. sin(3PI/2) = -1, and cos(3PI/2) = 0 so cot(3PI/2) = 0 = cot(15PI/2) = cot(3PI/2 + 2nPI) where n is any integer. csc(PI) = 1/sin(PI) which is undefined, since sin(PI) = 0. csc(PI + 2nPI) for any integer value n will be undefined. You can translate between real values (radians) and angles as arguments for the trigonometric functions using 2PI = 360 degrees. So PI = 180 degrees and 3PI/2 = 270 degrees, but this can be confusing if you are thinking of the trig functions as being defined as ratios of the sides of right triangles, since you cannot draw triangles with angles of 180 or 270 degrees. To appreciate them as periodic functions you must really use a definition that yeilds values for all real numbers (except in those cases for tan, cot, sec and csc where they are undefined). Generally this is done using a unit circle centered at the origin, where the independent variable in radians is the distance from the point on the circle at (1,0), measured along the arc (including any number of full circles equal to 2PI). IF we let w be this independent variable, and the point on the circle w radians from (1,0) be represented by (xsubw, ysubw), then sin(w) = ysubw and cos(w) = xsubw tan(w) = ysubw/xsubw, cot = xsubw/ysubw etc. Of course, when the denominator is zero, the function is not defined. This definition makes the functions easy to determine for quadrantal angles like 90 degrees (0 , 1) or 180 degrees (-1, 0), or 270 degrees (0, -1).
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