cos(0.2) with the relation (photo)(with 10 and 50 terms) and direct function exponential;observe a relationship recurrence between 2 terms successive Ti+1 and T1.
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In “observe a relationship recurrence between two successive terms, Ti+1 and T1 ” I believe you are being asked how the n+1-st term relates to the n-th term in the series for cosine. Note that if (-1)^n*x^(2*n)/(2*n)! is one term and (-1)^(n+1)*x^(2*(n+1))/(2*(n+1))! is the next term then the second is equal to the first multiplied by -x^2/((2*n+1)*(2*n+2)).
Is this homework? Don't compare the small latest term you are adding on (say 0.003) to the whole sum (say .707 for 45 degrees). Those are the wrong things to compare. Either compare the sum to the true value (sind(angle)) or compare your latest term to the prior term, which means you'd have to make term an array.
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