The Laplace transform of sin^2t is equal to 1/2s – s/(2s^{2}+8). In this article, we will learn how to find the Laplace of sin square t. The formula of the Laplace of sin^{2}t is given below:

L{sin^{2}t} = 1/2s – s/(2s^{2}+8).

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## Find the Laplace Transform of sin^{2}t

**Answer:** The Laplace transform of sin square t is 1/2s – s/(2s^{2}+8).

*Proof:*

It is known from trigonometry that 1-cos2t=2sin^{2}t. Therefore, we have

sin^{2}t = $\frac{1}{2}$(1-cos2t)

Now, we take the Laplace transforms on both sides of the above equation. By doing so, we get that

L{sin^{2}t} = L{$\frac{1}{2}$(1-cos2t)}.

Applying the linearity property of Laplace transforms,

L{sin^{2}t} = $\frac{1}{2}$ (L{1} – L{cos2t}).

We know that the Laplace Transform of 1 is 1/s and the Laplace transform of cos 2t is s/(s^{2}+4). Hence, it follows that

L{sin^{2}t} = $\dfrac{1}{2} \left(\dfrac{1}{s}-\dfrac{s}{s^2+4} \right)$

Simplifying we obtain that

L{sin^{2}t} = $\dfrac{1}{2s}-\dfrac{s}{2(s^2+4)}$

Therefore, the Laplace transform of sin^2t is equal to 1/2s – s/(2s^{2}+8).

**Main Article:** Laplace Transform: Definition, Table, Formulas, Properties

Laplace tansform of a constant

## FAQs

**Q1: What is the Laplace transform of sin^2t?**

Answer: The Laplace transform of sin^2t is equal to 1/2s – s/(2s^{2}+8). That is, L{sin^{2}t} = 1/2s – s/(2s^{2}+8).

This article is written by Dr. T. Mandal, Ph.D in Mathematics. On Mathstoon.com you will find Maths from very basic level to advanced level. Thanks for visiting.