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Solve the given problems.A water slide at an amusement park follows the curve $(y \text { in } m$ ) $y=2.0+2.0 \cos (0.53 x+0.40)$ for $0 \leq x \leq 5.0 \mathrm{m} .$ Find theangle with the horizontal of the slide for $x=2.5 \mathrm{m}$

Calculus 1 / AB

Chapter 27

Differentiation of Transcendental Functions

Section 1

Derivatives of the sine and Cosine Functions

Derivatives

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University of Michigan - Ann Arbor

University of Nottingham

Boston College

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for this problem here we have a water slide at an amusement park and it follows the following curve. Said to me why equals two plus to co sign 0.53 X-us 0.40. So that's gonna be our graph here and we're going to have some radiant again. And um That's from Zurich five. Should we want to find the angle with the horizontal of the slide for x equals 2.5. So to do that we take the derivative of this. So if this is F of X, we want to take a Crime of acts. We want to evaluate it when access 2.5. So we see that f crime of 2.5. Anyway, it's about a negative 1.05. So we see it 2.5 right here we have about a negative one slope. So the angle that makes with the horizontal of the slide would be about a negative 45 degrees. Um or negative .808 radiance. That would be our final answer. And again, that's because a negative 0.808 ratings. If we multiply that times 21 80 divided by pi, we get about, as we said, a negative 45 degrees. In this case it will be negative 46 degrees approximately. So that's our final answer.

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The number 2 is also the smallest & first prime number (since every other even number is divisible by two).

If you write pi (to the first two decimal places of 3.14) backwards, in big, block letters it actually reads "PIE".

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