(1) Trigonometry 9

(1) Trigonometry 9 - Pre Calculus Math 40S Explained...

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Pre – Calculus Math 40S: Explained! www.math40s.com 83 Trigonometry Lesson 9 Part I - Graphing Other Trig Functions Graphing y = tan θ & y = cot θ The vertical lines you see are called asymptotes . They are places where the graph is undefined. Recall that θ θ θ θ θ θ sin cos tan = and cot = cos sin tan θ is undefined at the angles where cos θ is equal to zero. π π 3 , 2 2 Likewise, cot θ is undefined whenever sin θ is equal to zero. [ ] π 0, It is important you state the general solution of the asymptotes for each graph. y = tan θ For tan θ , we can see from the graph that the first positive asymptote occurs at 2 π . All asymptotes are exactly π units away from each other. The general equation of the asymptotes is: π π x = ±n 2 a-value: We only use the term amplitude in describing the graphs of sin θ and cos θ . The other four trig graphs are not “closed in”, they go up & down forever. So, we simply call the a-value the vertical stretch . b-value & period: IMPORTANT! The period of a basic tan θ or cot θ graph is π , not 2 π like sin θ and cos θ . Thus, we have the following formulas: Period = and b = b Pe y = cot θ riod π π c-value: No difference from sin θ and cos θ , but remember to move your asymptotes if you shift the graph. d-value: No difference from sin θ and cos θ . For cot θ , we can see from the graph that the first positive asymptote occurs at 0, and all asymptotes are exactly π units away from each other. The general equation of the asymptotes is: π π ± x = 0±n , or simply, x = n We always write the general solution of tan θ & cot θ asymptotes in the following way: x = Angle of first positive asymptote ± n(Period)
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Pre – Calculus Math 40S: Explained!
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  • Winter '10
  • KISCABEAN