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For what values of x in [0, 2pi] does the graph of Y= cos(x)/2+ sin(x)

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have a horizontal tangent? List the values of x below. Please explain?

asked Nov 1, 2014 in PRECALCULUS by anonymous

1 Answer

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The function y = cos(x)/2 + sin(x)

Differentiating on each side with respect to x.

y' = - sin(x)/2 + cos(x)

When the tangent line is horizontal, the slope is equal to 0.

That means, need to solve for y' = 0

- sin(x)/2 + cos(x) = 0

cos(x) = sin(x)/2

2 = sin(x)/cos(x)

tan(x) = 2

x = tan-1(2)

x = 63.43

The genaral solution of tan(x) = tan(α) is x = nπ + α, where n is an integer.

x = nπ + 63.43

For n = 0, x = 0(180) + 6 3.43

x = 63.430

For n = 2,x = 1(180) + 63.43

x = 243.430

For n = 2, x = 2(180) + 63.43

x = 423.430

The solutions on the interval [0, 2π] are x = 63.430 and 243.430.

answered Nov 1, 2014 by david Expert

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