Find the equation of the tangent line to the curve y=2sinx

1 answer:

8 0

Hello
f(x) = 2sin(x)
f(<span>π/6) = 1
f'(x) 2cos(x)
f'(</span>π/6) = 2×co(π/6) = 2 × root(3)×0.5 =root(3)
The equation of this tangent line is : y= root(3)(x-π/6)+1
y = root(3)x+1 - π/6(root(x)) <span>in the form y=mx+b
m = root(3) and b = </span>1 - π/6(root(x))

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Question:

Points (−6, 3) and (−6, −3) on the coordinate grid below show the positions of two dogs at a park.There is a point at (−6, 3) labeled Dog 1. There is a point at (−6, −3) labeled Dog 2.

Which statement best describes the relationship between the positions of the two players?

A.Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

B.Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

C.Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.

D. Dog 1's position is Dog 2's position reflected across the y-axis; only the signs of the x-coordinates of Dog 1 and Dog 2 are different.

Answer:

Option B: Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.

Explanation:

The position of the Dog 1 is (−6, 3).

The position of the Dog 2 is (−6, -3).

From the graph, we can see that the image of Dog 1 is reflected over x-axis. Because to reflect an image over x-axis, the signs of y-coordinate must be changed.

Hence, Option B is correct.

Thus, Dog 1's position is Dog 2's position reflected across the x-axis; only the signs of the y-coordinates of Dog 1 and Dog 2 are different.