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Maple Arctangent Function: Viewing Angle Calculation and Distance Estimation

Learn how to calculate viewing angles using Maple's arctan function, estimate distances to screen rows, and adjust calculations for new screen measurements. Steps include evaluating functions, plotting values, and approximating results accurately.

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Maple Arctangent Function: Viewing Angle Calculation and Distance Estimation

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  1. CS 121 – Quiz 2 Question 5

  2. Question 5 a) The arctangent function in Maple is arctan. b) To find the viewing angle, evaluate the given function θ(x) at the given point. Maple will give an exact answer, so you will have to approximate this to 10 decimal places.

  3. c) We are given that the first row is a feet from the screen and each row is b feet apart. We can then define the distance x for a certain row r by assigning x := a + b  (r – 1) - We can then evaluate θ(x), which will give us a function of r. We can then plot this, and estimate the value of r at the maximum. We can check this by assigning nearby values to r, evaluating θ, and choosing the value that truly is the maximum. d) Calculate the distance of that row to screen, plug it in to expression on step b in place of x.

  4. e) New measurements for the screen are given, with the screen being f feet tall and g feet off of the ground. - We can redefine θ to bearctan((f + g) / x) – arctan(g / x) and solve similarly to part b. f) Similar to part c, using the new θ. g) Similar to part d, using the new θ.

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