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Question 3.52) Consider the curves y = f(x)=x² and y= g(x)=(x-2)² -2. Find the acute angle of intersection between the curves. Procedure:-Find the point of intersection. - Find the slope of both tangents lines at that point. - Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line makes with the x-axis. - Conclude.

Question 3.52) Consider the curves y = f(x)=x² and y= g(x)=(x-2)² -2. Find the acute angle of intersection between the curves. Procedure:-Find the point of intersection. - Find the slope of both tangents lines at that point. - Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line makes with the x-axis. - Conclude.

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
8th Edition
ISBN:9781305652224
Author:Charles P. McKeague, Mark D. Turner
Publisher:Charles P. McKeague, Mark D. Turner
Chapter2: Right Triangle Trigonometry
Section: Chapter Questions
Problem 1RP: The origins of the sine function are found in the tables of chords for a circle constructed by the...
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Can you please answer question 3.52
Question 3.51) Find the value of the following. Make sure to show the data in the unit circle and/or in right triangles to justify your answers. A) arcsin (2) B) arccos (-√2) C) arctan(-Ys) D) arccot (cot(-3)) E) sec (arccsc()) (Use a right triangle). Question 3.52) Consider the curves y = f(x)=x² and y= g(x)=(x−2)² - 2. Find the acute angle of intersection between the curves. Procedure:-Find the point of intersection. - Find the slope of both tangents lines at that point. - Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line makes with the x-axis. - Conclude. Question 3.53) Differentiate the following functions. Simplify your answers as much as possible. A) arccos (3x) B) xsin ¹(x²) t sec-1 D) arccsc(- E) sin (arccot(x²)) (remember to simplify...) Question 3.54) Using a chain rule, show how one obtains the derivative of arccosx. Question 3.55) A) [sin¯¹(1-r¹)]² Differentiate the following functions. Simplify your answers as much as possible. B) cos³ (csc ¹ (²+2)) (remember to simplify...) C) tan (√r arccos(√r)) cot ¹(x³) csc(x³) D) Question 3.56) Some "review" questions... A) Evaluate or simplify the following much as you can. Show the steps: no calculator, use the definition and properties of logarithms. i) log 27 (243) ii) log(2300)-In (23) iii) e²ln√x+1 In(10) B) Solve the following equations for x. Give both an exact value as well as a decimal approximation from the calculator. i) 4²x+¹=3.5* ii) log (In x) = 2
Transcribed Image Text:Question 3.51) Find the value of the following. Make sure to show the data in the unit circle and/or in right triangles to justify your answers. A) arcsin (2) B) arccos (-√2) C) arctan(-Ys) D) arccot (cot(-3)) E) sec (arccsc()) (Use a right triangle). Question 3.52) Consider the curves y = f(x)=x² and y= g(x)=(x−2)² - 2. Find the acute angle of intersection between the curves. Procedure:-Find the point of intersection. - Find the slope of both tangents lines at that point. - Use an inverse trigonometric f" (show this clearly) to find the angle that each tangent line makes with the x-axis. - Conclude. Question 3.53) Differentiate the following functions. Simplify your answers as much as possible. A) arccos (3x) B) xsin ¹(x²) t sec-1 D) arccsc(- E) sin (arccot(x²)) (remember to simplify...) Question 3.54) Using a chain rule, show how one obtains the derivative of arccosx. Question 3.55) A) [sin¯¹(1-r¹)]² Differentiate the following functions. Simplify your answers as much as possible. B) cos³ (csc ¹ (²+2)) (remember to simplify...) C) tan (√r arccos(√r)) cot ¹(x³) csc(x³) D) Question 3.56) Some "review" questions... A) Evaluate or simplify the following much as you can. Show the steps: no calculator, use the definition and properties of logarithms. i) log 27 (243) ii) log(2300)-In (23) iii) e²ln√x+1 In(10) B) Solve the following equations for x. Give both an exact value as well as a decimal approximation from the calculator. i) 4²x+¹=3.5* ii) log (In x) = 2
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