(Solved): carring out arithmetic operations with complex numbers to answer these questions As you've seen in c ...

As you've seen in class, when values of $$?$$ are small approximations are sometimes used for trig functions $$\sin ?,\cos ?$$ and $$\tan ?$$. 1) For each trig function: State what approximation is used. Using a graph or graph to illustrate write a few sentences to explain why each approximation is appropriate. NB. Remember to measure $$?$$ in radians. 2) Choose one Trig function a. For selected small values of $$?$$ calculate the difference between the true trig value and the approximated value. Then calculate this difference as a percentage of the true trig value - to give you the percentage error. (ie. How inaccurate is the approximation for this size of angle) b. Plot a graph of percentage error against $$?$$. c. Interpolate from your graph the maximum permissible angle that its OK to use approximations for if you can tolerate i) $$1\%$$ error, ii) $$0.5\%$$ error, iii) $$0.1\%$$ error 3) Write a paragraph to explain what you can conclude from your investigation. NB. Your graphs may be hand-drawn or produced using any graph plotting software you are familiar with. Ensure that graphs are clearly titled and axes are clearly labelled, and scales chosen so as to clearly show what you intend to illustrate.