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In 2008 Petersen posed a list of questions on the application oftrans-quasiconformal Siegel surgery developed by Zakeri and himself. In thispaper we extend Petersen-Zakeri's idea so that the surgery can be applied toall the premodels which have no "free critical points". We explain how the ideais used in solving three of the questions posed by Petersen. To present thedetails of the idea, we focus on the solution of one of them: we prove that fortypical rotation numbers $0< \theta < 1$, the boundary of the Siegel disk of$f_{\theta}(z) = e^{2 \pi i \theta} \sin (z)$ is a Jordan curve which passesthrough exactly two critical points $\pi/2$ and $-\pi/2$.

On David type Siegel Disks of the Sine family