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Chapter 8 Test Thursday Friday Graphing Sine/Cosine Equations (2)
Write Equation of Sine/Cosine Graph (2) Solve Trig Equations (6) Sinusoidal Word Problems (2) Friday Simplify Trig Expressions (3) Prove Trig Identities (2)
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Review 4. 5. Prove: Simplify: 1. 2. Solve for πβ€π½<ππ
: 6. 3. 7. 8.
9. 10. 4πππ 2π=3 3 π ππ 2 π+2π πππβ1=0 2 π ππ 2 π+π‘πππ=5
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Write a sine and cosine equation for each graph: Graph:
11. π¦= 1 4 π ππ 1 2 π₯+ π 4 12. π¦=3πππ 10π₯+1 13. 14.
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15. Water wheels are still used in lumber mills in historic recreations. A typical water wheel makes one complete revolution every 90 seconds. A paddle starts its cycle 1 meter below water level and reaches a maximum height of 4 meters above the water. Assume that the timing starts when the paddle is at the top of the water wheel. Sketch a graph that represents the paddleβs height with respect to time. Find a sinusoidal equation to model the height of the paddle. What is the height of the paddle at 21.2 seconds?
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Angle of inclination (degrees) = βππ.ππππ πππ πππ π+ππ +ππ
16. The angle of inclination of the sun changes throughout the year. This changing angle affects the heating and cooling of buildings. The overhang of a roof of a house is designed to shade the windows for cooling in the summer and allow the sunβs rays to enter the house for heating in the winter. The sunβs angle of inclination at noon in central New York state can be modeled by the formula: (x is the day number in the year) Angle of inclination (degrees) = βππ.ππππ πππ πππ π+ππ +ππ Find the sunβs angle of inclination at noon on Valentineβs Day (Day 45). Sketch a graph of the situation. What are the greatest and least angles of inclination at noon?
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βππ.ππππ πππ πππ π+ππ +ππ =33.26 =ππ.π =ππ.π c. ππ«ππππππ:ππ+ππ.π
βππ.ππππ πππ πππ π+ππ +ππ Valentineβs Day (Day 45) βππ.ππππ πππ πππ ππ+ππ +ππ =33.26 c. ππ«ππππππ:ππ+ππ.π =ππ.π πππππ:ππβππ.π =ππ.π
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