Using the double angle identities, find sin2x given sinx=4/5

  24/25

Step-by-step explanation:

The usual form of the double-angle identity is for sine is ...

  sin(2x) = 2sin(x)cos(x)

The cosine can be found from the sine using the Pythagorean identity ...

  sin(x)² + cos(x)² = 1

  cos(x) = √(1 -sin(x)²)

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Filling in the given value for sin(x), we can find the cosine to be ...

  cos(x) = √(1 -(4/5)²) = √(9/25) = 3/5 . . . . . . . assuming a first-quadrant angle

Then the desired sine is ...

  sin(2x) = 2sin(x)cos(x) = 2(4/5)(3/5)

  sin(2x) = 24/25

answer: you have to send a photo of the question

step-by-step explanation:

maximum area = xy = (16)(32) = 512 ft2

to maximize the area of the garden, the side of the fence parallel to the side of the house should be 32 ft long, and the other two sides should both have length 16 ft.'

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