Final answer:
The number of terms from the Maclaurin series needed to approximate cos x to 8 significant figures depends on the value of x, with fewer terms needed for smaller values of x. Exact determination requires a specific value of x.
Step-by-step explanation:
The question asks us to determine the number of terms necessary to approximate cos x to 8 significant figures using the Maclaurin series for the cosine function. The Maclaurin series for cos x is given by cos x = 1 - x^2 / 2! + x^4 / 4! - x^6 / 6! + ... where higher-order terms continue in the pattern of alternating signs, and factorial denominators.
To approximate cos x to 8 significant figures, we need to add terms from the series until the absolute value of the next term is less than 0.5 * 10^-(8), which is the precision required for 8 significant figures. Typically, this approximation depends on the value of x. When x is small, fewer terms will be required because the factorial in the denominator grows very fast, making the terms rapidly converge to 0. However, without a specific value of x, we are unable to provide the exact number of terms. Generally speaking, as x approaches 0 (such as at x=0°), the first term (1) alone gives an 8-significant-figure approximation as cos(0)=1.