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I know $\cos^2(t) + \sin^2(t) = 1 $, but I don't know what it gives when there is a minus in one and plus in the other. I have tried googling, but I found no answer. Thank you for answering :)

2017年10月1日 · So, I know that $sin^2(t)$ is an even function so the $b_{n}$ co-efficient's are 0 and that we will only be figuring out the $a_{n}$ and the $a_{0}$ co-efficient's ...

2020年9月13日 · I know from L'Hopital's Rule that $$\lim_{t \to 0} \frac{t^2} {\sin^2(t)}=1$$ But I'm also trying to verify this using the Squeeze Theorem. My first thought is to use the upper and lower bounds of possible outputs (range) of $\sin^2(t)$ as the functions which $\sin^2(t)$ would be between: $$ 0 \leq \sin^2(t) \leq 1 $$

Using this approach, I get the answer $\ln(\sin^2(t))(\sin^2t)^t\sin 2t$, which is different from the correct answer $2(\sin^2t)^t(\ln\sin t+t\cot t)$. I understand why this answer is correct using logarithmic differentiation.

I've thought of just working through the integral and then taking the derivative of the answer, but I don't have a clue how to integrate $\sin t^2$ (not $\sin^2t$). I'm not sure if this is even integrable.

Stack Exchange Network. Stack Exchange network consists of 183 Q&A communities including Stack Overflow, the largest, most trusted online community for developers to learn, share their knowledge, and build their careers.

$$ 1 - \frac{t^2}{3!} + \frac{t^4}{5!} - \frac{t^6}{7!} + O(t^8)$$ The problem is that I'm awful at anything involving power series. I have no idea how I'm supposed to continue here. I've tried using the definition of the Laplace Transform and solving the integral $$\int_0^\infty e^{-st}*\frac{sin(t)}{t} dt$$

2020年9月6日 · Because there are many cases where we want powers of trig functions, we define $\sin^2(x)=(\sin(x))^2$.It doesn't have to be that way.