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The Three Trig Functions… and Their R eciprocals

Start!. The Three Trig Functions… and Their R eciprocals. 11 th grade Trigonometry Ms. Kavanaugh. Click on a graph to learn more about the trig functions: . tangent. cosine. sine. cosecant. secant. cotangent. Properties of a trig function :. Review Question. a mplitude. period.

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The Three Trig Functions… and Their R eciprocals

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  1. Start! The Three Trig Functions…and Their Reciprocals 11th grade Trigonometry Ms. Kavanaugh

  2. Click on a graph to learn more about the trig functions: tangent cosine • sine cosecant secant cotangent Properties of a trig function: Review Question amplitude period

  3. Sine Back to main menu (sin) The period for the sine graph is 2, meaning the graph completes one whole wave every 2. The normal sine graph, for one period, begins at the origin, (0,0), and ends at the point (2,0). The amplitude of the sine function is 1. It’s maximum on the y-scale is 1 and the minimum is -1.

  4. Cosine Back to main menu (cos) The period for the cosine graph is 2, meaning the graph completes one whole wave every 2. The normal cosine graph, for one period, begins at (0,1) and ends at the point (2,1). The amplitude of the cosine function is 1. It’s maximum on the y-scale is 1 and the minimum is -1.

  5. Tangent Back to main menu (tan) The period of the tangent graph is . Meaning the graph completes one whole wave every . Unlike the sine and cosine functions, tangent does not have an amplitude. Instead the function has asymptotes one intervals of . This happens because of the definition of tan x. When cos x =0, the graph is undefined causing an asymptote. Remember: Tan x = sinx/cosx

  6. Cosecant Back to Main menu (csc) The cosecant graph has a period of 2. Meaning it completes one wave every 2. Similarly to the tangent graph, the csc graph has vertical asymptotes. This happens because of the definition of cscx. When sinx=0, the graph is undefined causing an asymptote. Because of these asymptotes, the cosecant graph does not have an amplitude. Remember: Csc x = 1/sinx sine cosecant

  7. Secant Back to main menu (sec) The secant graph has a period of 2. Meaning it completes one wave every 2. Similar to the tangent graph, the sec graph has vertical asymptotes. This happens because of the definition of sec x. When cosx=0, the graph is undefined causing an asymptote. Because of these asymptotes, the secant graph does not have an amplitude. Remember: secx= 1/cosx secant cosine

  8. Cotangent Back to mainmenu The cotangent graph has a period of . Meaning the graph completes one whole wave every . Like its reciprocal, the cotangent has vertical asymptotes. This happen because of the definition of cotangent, when sinx =0 the function is undefined causing an asymptote. Because of these asymptotes, the cotangent graph does not have an amplitude. Remember: cotx=cosx/sinx tangent cotangent

  9. Amplitude Back to Main menu Amplitude is the height of the wave. The amplitude works in both directions. Every wave has a positive amplitude, meaning you take the absolute value of the amplitude of the wave. The amplitude works in both directions. The amplitude is usually written as a numerical value in front of the function.

  10. Period Back to mainmenu The period of the function is the length in which it takes the graph one wave to complete. The period for sine, cosine, cosecant, and secant is found by the equation 2/b. The period of the tangent and cotangent is found by using /b. Where in both cases b is the numerical value found directly after the function, usually contained inside the parenthesis.

  11. Review Question: What is the function of this graph? A. y= 3sin2x B. y= 6tan3x C. y= 3cos2x

  12. Close… but try again! Back to question Remember that the sine functions starts at the origin. For this function the amplitude is 3 and the period is . Go back to the question and give it another try!

  13. Almost, give it another go! Back to question Remember that the tangent function has vertical asymptotes. There is no amplitude for this function and the period is 3. Click the arrow to go back to the question and give it another go!

  14. Correct! Finish! This is a cosine function with an amplitude of 3, and a period of . Click the arrow to finish this lesson.

  15. Well Done! Congratulations, you’ve completed this lesson on the three trig functions and their reciprocals! Click the star to go back to the main menu.

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