Chapter 1.5, Problem 95E

(a)

To determine

To calculate: The value of $\sin \frac{1}{2}$ if its polynomial approximation is given as $\sin x\approx x-\frac{x^3}{3!}+\frac{x^5}{5!}$ and then compare the value of $\sin \frac{1}{2}$ obtain from approximation with the value of $\sin \frac{1}{2}$ obtain from calculator. Also, estimate whether the error in the examination is same or not.

(b)

To determine

To calculate: The value of $\sin 1$ if its polynomial approximation is given as $\sin x\approx x-\frac{x^3}{3!}+\frac{x^5}{5!}$ and then compare the value of $\sin 1$ obtain from approximation with the value of $\sin 1$ obtain from calculator. Also, estimate whether the error in the examination is same or not.

(c)

To determine

To calculate: The value of $\sin \frac{\pi }{6}$ if its polynomial approximation is given as $\sin x\approx x-\frac{x^3}{3!}+\frac{x^5}{5!}$ and then compare the value of $\sin \frac{\pi }{6}$ obtain from approximation with the value of $\sin \frac{\pi }{6}$ obtain from calculator. Also, estimate whether the error in the examination is same or not.

(d)

To determine

To calculate: The value of $\cos \left(-0.5\right)$ if its polynomial approximation is given as $\cos x\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}$ and then compare the value of $\cos \left(-0.5\right)$ obtain from approximation with the value of $\cos \left(-0.5\right)$ obtain from calculator. Also, estimate whether the error in the examination is same or not.

(e)

To determine

To calculate: The value of $\cos 1$ if its polynomial approximation is given as $\cos x\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}$ and then compare the value of $\cos 1$ obtain from approximation with the value of $\cos 1$ obtain from calculator. Also, estimate whether the error in the examination is same or not.

(f)

To determine

To calculate: The value of $\cos \frac{\pi }{4}$ if its polynomial approximation is given as $\cos x\approx 1-\frac{x^2}{2!}+\frac{x^4}{4!}$ and then compare the value of $\cos \frac{\pi }{4}$ obtain from approximation with the value of $\cos \frac{\pi }{4}$ obtain from calculator. Also, estimate whether the error in the examination is same or not.