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ss_5_3 - Section 5.3 Properties of Trigonometric Functions...

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Section 5.3 Properties of Trigonometric Functions In this section, we cover some of the fundamental properties of the six basic trig functions. We note that the sine and cosine are defined for all real numbers, but there are isolated points where the other four trig functions are not defined. The range of the sine function and cosine function is the interval [ - 1 , 1]; so, an equation like sin x = 2 will not have a solution. We begin by giving the domains and ranges and graphs of the six trig functions. Function sin θ cos θ tan θ Domain ( -∞ , ) ( -∞ , ) x 6 =(2 n +1) π 2 Range [-1,1] [-1,1] ( -∞ , ) Function csc θ sec θ cot θ Domain x 6 = x 6 n π 2 x 6 = Range ( -∞ , - 1] [1 , ) ( -∞ , - 1] [1 , ) ( -∞ , ) Graphs of the Six Trigonometric Functions One should note from the following graphs that the graphs of the secant, cotangent, and cosecant can be obtained from the graphs of cosine, tangent, and sine, using the fact that the first three functions are reciprocals of the second three functions. –1 –0.5 0 0.5 1 24681 01 2 t –1 –0.5 0 0.5 1 2 t –10 –8 –6 –4 –2 0 2 4 6 8 10 y 2 t –3 –2 –1 0 1 2 3 y 2 t –10 –8 –6 –4 –2 0 2 4 6 8 10 y 2 t –3 –2 –1 0 1 2 3 y 2 t Periods of Trigonometric Functions One can see from the graphs of sine and cosine that these two functions have graphs that repeat periodically. Functions that repeat in this manner are called periodic functions. The notion of periodicity is made precise below. Note in the following that sin
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This note was uploaded on 12/11/2011 for the course MAC 1140 taught by Professor Kutter during the Fall '11 term at FSU.

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ss_5_3 - Section 5.3 Properties of Trigonometric Functions...

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