Find all solutions of the equation correct to two decimal places

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SUMMARY

The equation tan x = √(4 - x²) requires finding solutions correct to two decimal places. The initial approach involves squaring both sides to obtain tan²x = 4 - x². To refine the solution, graphing both functions and applying Newton's method can be effective strategies. A graphing calculator confirmed the solutions after initial approximation.

PREREQUISITES
  • Understanding of trigonometric functions, specifically tangent.
  • Familiarity with square roots and their properties.
  • Basic graphing skills to plot functions accurately.
  • Knowledge of numerical methods, particularly Newton's method.
NEXT STEPS
  • Learn how to graph trigonometric functions using graphing calculators.
  • Study Newton's method for finding roots of equations.
  • Explore the properties of the tangent function and its periodicity.
  • Investigate numerical approximation techniques for solving equations.
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Students studying mathematics, particularly those tackling trigonometric equations, as well as educators looking for effective teaching methods in numerical analysis.

fillipeano
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Homework Statement


Find all solutions of the equation correct to two decimal places.
tan x = \sqrt{4 − x^2}


Homework Equations





The Attempt at a Solution


I squared both sides, giving me tan^2x = 4 - x^2, but I don't know where to go from there.
 
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fillipeano said:

Homework Statement


Find all solutions of the equation correct to two decimal places.
tan x = \sqrt{4 − x^2}


Homework Equations





The Attempt at a Solution


I squared both sides, giving me tan^2x = 4 - x^2, but I don't know where to go from there.

(1) Draw a (rough) graph of tan x and of sqrt(4-x^2) on the same plot. This will give you
an approximate solution.
(2) If necessary, correct the rought solution from (1) using Newton's method, for example (among many, many possible available methods).

RGV
 
I wasn't sure what I was supposed to do when I posted this. Thank you for clarifying, I used a graphing calculator and got the answer.
 

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