Questions: f(x) = cos(2x) on [-π/4, π/4]

Solution Steps

To solve the problem of evaluating the function \( f(x) = \cos(2x) \) over the interval \(\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]\), we can generate a set of \( x \) values within the given interval and compute the corresponding \( f(x) \) values.

We are given the function \( f(x) = \cos(2x) \) and the interval \(\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]\). We need to evaluate \( f(x) \) at various points within this interval.

We generate 100 equally spaced \( x \) values within the interval \(\left[-\frac{\pi}{4}, \frac{\pi}{4}\right]\).

For each \( x \) value, we compute \( f(x) = \cos(2x) \).

We present the computed values of \( f(x) \) for the generated \( x \) values. Here are some of the results:

\[ \begin{align_} f(-0.7854) & = 6.1232 \times 10^{-17} \\ f(-0.7695) & = 0.03173 \\ f(-0.7537) & = 0.06342 \\ f(-0.7378) & = 0.09506 \\ f(-0.7219) & = 0.1266 \\ f(-0.7061) & = 0.1580 \\ f(-0.6902) & = 0.1893 \\ f(-0.6743) & = 0.2203 \\ f(-0.6585) & = 0.2511 \\ f(-0.6426) & = 0.2817 \\ f(-0.6267) & = 0.3120 \\ f(-0.6109) & = 0.3420 \\ f(-0.5950) & = 0.3717 \\ f(-0.5791) & = 0.4009 \\ f(-0.5633) & = 0.4298 \\ f(-0.5474) & = 0.4582 \\ f(-0.5315) & = 0.4862 \\ f(-0.5157) & = 0.5137 \\ f(-0.4998) & = 0.5406 \\ f(-0.4839) & = 0.5671 \\ f(-0.4681) & = 0.5929 \\ f(-0.4522) & = 0.6182 \\ f(-0.4363) & = 0.6428 \\ f(-0.4205) & = 0.6668 \\ f(-0.4046) & = 0.6901 \\ f(-0.3887) & = 0.7127 \\ f(-0.3729) & = 0.7346 \\ f(-0.3570) & = 0.7557 \\ f(-0.3411) & = 0.7761 \\ f(-0.3253) & = 0.7958 \\ f(-0.3094) & = 0.8146 \\ f(-0.2935) & = 0.8326 \\ f(-0.2777) & = 0.8497 \\ f(-0.2618) & = 0.8660 \\ f(-0.2459) & = 0.8815 \\ f(-0.2301) & = 0.8960 \\ f(-0.2142) & = 0.9096 \\ f(-0.1983) & = 0.9224 \\ \end{align_} \]

Final Answer