- #1
Evangeline101
- 112
- 5
Homework Statement
Homework Equations
none
The Attempt at a Solution
-amplitude is 3
-period is 180°
-right 60°
-down 1
Rough sketch of graph:
Thanks :)
blue_leaf77 said:You got it wrong. That's the graph of y=−3sin(2(x−60o))−1y=−3sin(2(x−60o))−1y = -3\sin(2(x-60^o))-1.
Ok I have attempted the graph again:blue_leaf77 said:Still incorrect. Start from f(x)=3sin(2(x−60o))f(x)=3sin(2(x−60o))f(x) = 3\sin(2(x-60^o)) which can be obtained by translating f(x)=3sin(2x)f(x)=3sin(2x)f(x) = 3\sin(2x) to [left/right, it's your part to answer] by 60o60o60^o degrees.
blue_leaf77 said:Your first drawing is almost correct. It's just the negative sign in front of the sine function that needs to be removed.
blue_leaf77 said:Yes, that's the correct one.
Sinusoidal functions are a type of mathematical function that describes the behavior of a wave. They are characterized by the presence of a repeating pattern or cycle, and are often used to model natural phenomena such as sound waves, light waves, and alternating current.
Transformations in sinusoidal functions refer to changes made to the basic shape and position of the function. These transformations can include changes in amplitude, period, phase shift, and vertical shift. They allow us to manipulate and customize the behavior of the function to fit specific data or situations.
To sketch a graph of a sinusoidal function, you will need to identify the key features of the function, including the amplitude, period, phase shift, and vertical shift. Then, plot these points on a graph and connect them with a smooth curve. It can also be helpful to plot additional points to ensure accuracy and to label the x and y axes.
The graph of a sinusoidal function is directly related to its equation. The amplitude is represented by the coefficient of the sine or cosine function, the period is determined by the coefficient in front of the variable inside the parentheses, and the phase shift and vertical shift are represented by the values added or subtracted at the end of the equation.
Sinusoidal functions have many practical applications in the real world. They can be used to model and predict the behavior of waves, such as sound or light waves. They are also commonly used in engineering and physics to describe the behavior of electrical currents and mechanical oscillations. Additionally, sinusoidal functions are used in fields such as economics and biology to analyze and predict natural and economic cycles.