Calculus #7: Calculate $\sin(\frac{\pi}{180} \times 68)$ without calculator.

You may want to solve this and this problem first.

Consider the definition of a Taylor's Series :

$f(x) = f(a)+\frac {f'(a)}{1!} (x-a)+ \frac{f''(a)}{2!} (x-a)^2+\frac{f^{(3)}(a)}{3!}(x-a)^3+ \cdots.$

Notation: $f^{(n)}(a)$ refers to the 3rd derrivative of the function $f$ into which value $a$ is entered.

Find $\sin(\frac{\pi}{180} \times 68)$ without using a calculator accurate to 2 decimal places.

Hint: It is easier if $a = 0$ .

See more calculus problems .