Answer:
- See the graphs attached and the explanation below
Explanation:
The most simple sine function, considered the parent function, is:
      
That function has:
- Midline, also known as rest or equilibrium position: y = 0
- Minimum: - 1
- Maximum: 1
- Amplitude: the distance between a minimum or a maximum and the midline = 1
- period: the interval of repetition of the function = 2π
The more general sine function is:
              
That function has:
- Midline: y = D (it is a vertical shift from the parent function)
- Minimum: - A + D
- Maximum: A + D
- Amplitude: A
- period: 2π/B
- phase shift: C (it is a horizontal shift of the from the parent function)
Now, you have to draw the sine function with the given key features:
- Period = 4 ⇒ 2π/B = 4 ⇒ B = π/2
- midline y = - 1 ⇒ D = - 1
Substitute the know values and use the y-intercept to find C:
        
             
Substitute (0, -1)
               
               
Hence, the function to graph is:
               
To draw that function use this:
- Maxima: 3(1) - 1 = 3 - 1 = 2, at x = 1 ± 4n (n = 0, 1, 2, 3, ...)
- Minima: 3(-1) - 1 = - 3 - 1 = -4
- y-intercept: (0, - 1)
- x-intercepts: the solutions to 0 = 3sin(πx/2) = - 1
- first point of the midline: (0, -1) it is the same y-intercept
With that you can understand the graphs attached.
 
        
             
        
        
        
Answer: 358 square units
Steps:
(12 * 20) + (10 * 10) + (6 * 3)
240 + 100 + 18
358
        
             
        
        
        
OK 100% of doctors in the mid-1800s found to be correct and all surgeries
        
             
        
        
        
Answer:
60°
Step-by-step explanation:
90°+30°=120°
180°_120°=60°
 
        
                    
             
        
        
        
120 ft... a flat vertical line is 180 degrees, and since this is a 30,60,90 triangle, your equation is... 180-60=distance John is to the base