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section 13.6b

section 13.6b. Sine & Cosine Periodic Functions. Def : If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ. Trig functions defined using the unit circle are called circular functions.

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section 13.6b

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  1. section 13.6b Sine & Cosine Periodic Functions

  2. Def: If the terminal side of an angle is in standard position and intersects the unit circle at P(x,y) then x = cos Ɵ and y = sin Ɵ Trig functions defined using the unit circle are called circular functions.

  3. I. Graph y = sin Ɵ using the unit circle Periodic Function Circular Function 1 0   -1 0o 90o 180o 270o 360o Sin 

  4. Graph of the Sine (Degree Mode) The cycle starts to repeat ? The cycle starts ?

  5. Graph of the Sine (Radian Mode) The cycle starts ? The cycle starts to repeat ?

  6. Graph of the Cosine (Radian Mode) The cycle starts ? The cycle starts to repeat ?

  7. 5. Find the period of the Periodic Function The cycle ends ? The cycle starts ?

  8. 6. Find the period for each Periodic Function

  9. Find the exact value of each 7.) 8.)

  10. 9.) When a string is plucked on a harp, it is displaced from a fixed point to the middle of the string and vibrates back and forth, producing a musical tone. The exact tone depends on the frequency, or number of cycles per second, the string vibrates. Middle C has a frequency of 278 cycles per second or 278 hertz.

  11. 9.) continued: Middle C has a frequency of 278 cycles per second or 278 hertz. • What is the period? • Graph the function: Time in seconds displacement

  12. Homework Page 808 Problems: #11-28 all

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