1. 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)

2. Review 4. 5. Prove: Simplify: 1. 2. Solve for 𝟎≤𝜽<𝟐𝝅: 6. 3. 7. 8.9.
10.
4𝑐𝑜𝑠2𝜃=3
3 𝑠𝑖𝑛 2 𝜃+2𝑠𝑖𝑛𝜃−1=0
2 𝑠𝑒𝑐 2 𝜃+𝑡𝑎𝑛𝜃=5

3. Write a sine and cosine equation for each graph: Graph:
11. 𝑦= 1 4 𝑠𝑖𝑛 1 2 𝑥+ 𝜋 4
12. 𝑦=3𝑐𝑜𝑠10𝑥+1
13.
14.

4. 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 paddle’s 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?

5. Angle of inclination (degrees) = −𝟐𝟑.𝟓𝒄𝒐𝒔 𝟑𝟔𝟎 𝟑𝟔𝟓 𝒙+𝟏𝟎 +𝟒𝟕
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 sun’s rays to enter the house for heating in the winter.
The sun’s 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) = −𝟐𝟑.𝟓𝒄𝒐𝒔 𝟑𝟔𝟎 𝟑𝟔𝟓 𝒙+𝟏𝟎 +𝟒𝟕
Find the sun’s angle of inclination at noon on Valentine’s Day (Day 45).
Sketch a graph of the situation.
What are the greatest and least angles of inclination at noon?

6. −𝟐𝟑.𝟓𝒄𝒐𝒔 𝟑𝟔𝟎 𝟑𝟔𝟓 𝒙+𝟏𝟎 +𝟒𝟕 =33.26 =𝟔𝟖.𝟓 =𝟐𝟏.𝟓 c. 𝐆𝐫𝐞𝐚𝐭𝒆𝒔𝒕:𝟒𝟓+𝟐𝟑.𝟓
−𝟐𝟑.𝟓𝒄𝒐𝒔 𝟑𝟔𝟎 𝟑𝟔𝟓 𝒙+𝟏𝟎 +𝟒𝟕
Valentine’s Day
(Day 45)
−𝟐𝟑.𝟓𝒄𝒐𝒔 𝟑𝟔𝟎 𝟑𝟔𝟓 𝟒𝟓+𝟏𝟎 +𝟒𝟕
=33.26
c. 𝐆𝐫𝐞𝐚𝐭𝒆𝒔𝒕:𝟒𝟓+𝟐𝟑.𝟓
=𝟔𝟖.𝟓
𝐋𝐞𝐚𝒔𝒕:𝟒𝟓−𝟐𝟑.𝟓
=𝟐𝟏.𝟓