How do you write the first four non-zero terms of the Maclaurin series for sin(x^2)?

1 Answer
May 7, 2018

sin (x^2) ~~ x^2 - x^6/3! + x^10/5! - x^14/7! + ...

Explanation:

Recall that the Maclaurin series for sin x is given by:

sin (x) ~~ x - x^3/3! + x^5/5! - x^7/7! + ...

Note: This is a common Maclaurin series and many exams require you to know this (which is why I directly referred to it). If you are not familiar with deriving Maclaurin series of any function (like y = sin x) I recommend that you read this

Hence, observing from the above approximation, we can replace x = x^2 in the formula to obtain:

sin (x^2) ~~ x^2 - x^6/3! + x^10/5! - x^14/7! + ...

Hope this helps! Comment below or PM me if you have any doubts!

All the best!