Describe how the graph of y + 3 = 2sin(3x + 90) compares to the graph of y = sin(x)
I suppose that 90 in your first equation is 90°
90°=(pi/2) radians
y+3= 2sin(3x +90°)
y=2sin(3x +90°)-3
y=2sin(3x +90°)-3 Angle in degres
y= 2sin(3x +pi/2)-3 Angle in radians
In google type:
"function graphs on line"
When you see list of results click on:
rechneronline.de/function-graphs/
When this page be open in blue rectacangle type:
2sin(3x + pi/2)-3
In gray rectacangle type:
sin(x)
Then click option Draw
You will see both graphs
On:
rechneronline.de/function-graphs/
In Dispay properties type follow values:
Range x-axis from -6.28 to 6.28
Range y-axis from -5.5 to 1.5
To describe how the graph of the equation y + 3 = 2sin(3x+90) compares to the graph of y = sin(x), we need to analyze the key differences and transformations applied to the original graph of y = sin(x).
1. Amplitude: The coefficient in front of the sin function determines the amplitude. In the equation y + 3 = 2sin(3x+90), the amplitude is 2, whereas in the graph of y = sin(x), the amplitude is 1. This means that the graph of y + 3 = 2sin(3x+90) will be "stretched" vertically by a factor of 2 compared to the graph of y = sin(x).
2. Period: The period of a sin curve is determined by the coefficient of x inside the sin function. In the equation y + 3 = 2sin(3x+90), the coefficient is 3, while in y = sin(x), it is 1. The period is calculated as (2π)/coefficient. Therefore, the period of y + 3 = 2sin(3x+90) is (2π)/3, which is one-third the period of y = sin(x). This implies that the graph of y + 3 = 2sin(3x+90) will be "compressed" horizontally compared to the graph of y = sin(x).
3. Phase Shift: The argument inside the sin function determines the horizontal shift or phase shift. In y + 3 = 2sin(3x+90), the phase shift is -90 degrees, or π/2 radians, to the left. This means that the graph of y + 3 = 2sin(3x+90) will be shifted horizontally π/2 units to the left compared to the graph of y = sin(x).
4. Vertical Shift: The constant term added or subtracted from the sin function influences the vertical shift. In y + 3 = 2sin(3x+90), the graph will be vertically shifted upward by 3 units compared to the graph of y = sin(x).
Overall, the graph of y + 3 = 2sin(3x+90) is a vertically stretched and horizontally compressed version of y = sin(x), shifted 3 units upwards and π/2 units to the left.