Determine the new coordinates of the point (π/6,√3/2) on the parent cosine function as it is transformed by the function g(x)=-4cos(1/3(x-π))
so plug in x=π/6 and calculate y.
or, apply the transformations
shift right by π
stretch x by 3
reflect across the x-axis
stretch y by 4
Thank you
To determine the new coordinates of a point on the parent cosine function after it has been transformed by the function g(x)=-4cos(1/3(x-π)), we need to follow a few steps:
1. Start with the original coordinates of the point, which are (π/6, √3/2).
2. Apply the transformation to the x-coordinate by subtracting π/6 from it: x-π/6.
3. Multiply the result from step 2 by 1/3: 1/3(x-π/6).
4. Apply the cosine function to the result from step 3: cos(1/3(x-π/6)).
5. Multiply the result from step 4 by -4: -4cos(1/3(x-π/6)).
6. The new x-coordinate is the same as the original one, which is π/6.
7. To find the new y-coordinate, evaluate the expression from step 5 using the new x-coordinate.
8. The new coordinates of the point are (π/6, y), where y is the result from step 7.
Let's calculate the new y-coordinate using the above steps:
Step 1: Original coordinates: (π/6, √3/2)
Step 2: x-π/6 = (π/6) - (π/6) = 0
Step 3: 1/3(0) = 0
Step 4: cos(0) = 1
Step 5: -4(1) = -4
Step 6: New x-coordinate: π/6
Step 7: Evaluate the expression from step 5: y = -4
Step 8: New coordinates: (π/6, -4)
Therefore, the new coordinates of the point (π/6, √3/2) on the parent cosine function transformed by the function g(x) = -4cos(1/3(x-π)) are (π/6, -4).