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What is the slope of the tangent line to y=cos(x)-2 at x=pi/2 ?

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gkstkdwl123 | Student, College Freshman | eNotes Newbie

Posted January 5, 2009 at 11:48 AM via web

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What is the slope of the tangent line to y=cos(x)-2 at x=pi/2 ?

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mcetner | High School Teacher | (Level 1) Adjunct Educator

Posted February 6, 2009 at 9:24 PM (Answer #1)

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The slope of the tangent line means derivative.  So, take the derivative of y = cosx - 2, and get dy/dx = -sinx.  Evaluate at pi/2, and -sin(pi/2) = -1.  So the slope of the tangent line at that point is -1.

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revolution | College Teacher | Valedictorian

Posted July 18, 2010 at 10:10 PM (Answer #2)

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The gradient of the tangent to the curve at any point is given by dy/dx. Get the slope of the equation, which is about -sinx. Subsitute in x= pi/2 and also inside -sinx in radian form, so the slope or the gradient of the tangent line is -1.

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tonys538 | TA , Undergraduate | Valedictorian

Posted September 27, 2014 at 4:42 AM (Answer #3)

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The slope of the tangent to the curve defined by y=cos(x)-2 at the point where x=pi/2 is required.

For a curve y = f(x), the slope of the tangent at x = a is equal to y'(a).

For y = cos x - 2, y' = -sin x

At x = pi/2, y' = 1

The required slope of the tangent is 1.

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