Unit for trigonometric functions is always radian. Problem 1 (10 points) The equation, cos(2x) = x,...

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Unit for trigonometric functions is always "radian". Problem 1 (10 points) The equation, cos(2x) = x, has a single real root near in the interval [0.0, 3.0]. Use the bisection method with an initial bracket [0.1, 1.3] to find the root. Specifically: take the first estimate of the root as 0.1; then (a) Perform the first 3 iterations by hand; (3 points) (b) Calculate the approximate relative percent error for each iteration; (3 points) (c) Calculate the tolerance for the final answer (the absolute value of the function f(x) valued at the approximate root); (1 point) (d) Use the bisection MATLAB code provided by the TA (and posted on Canvas) to find the root, with an acceptable relative percentage error equaling to or smaller than 0.001 (=0.001) (3 points) Unit for trigonometric functions is always "radian". Problem 1 (10 points) The equation, cos(2x) = x, has a single real root near in the interval [0.0, 3.0]. Use the bisection method with an initial bracket [0.1, 1.3] to find the root. Specifically: take the first estimate of the root as 0.1; then (a) Perform the first 3 iterations by hand; (3 points) (b) Calculate the approximate relative percent error for each iteration; (3 points) (c) Calculate the tolerance for the final answer (the absolute value of the function f(x) valued at the approximate root); (1 point) (d) Use the bisection MATLAB code provided by the TA (and posted on Canvas) to find the root, with an acceptable relative percentage error equaling to or smaller than 0.001 (=0.001) (3 points)