Parallax Formula
First of all, the astronomical unit is the AU, 1AU is equivalent to the distance between the Earth and the Sun. You can see in the image below that we know the angle and the distance between the Earth and the Sun. This is an important data because if we use Tg α= 1/d we can isolate the distance (d). This d is the distance between the Earth and the star that we want to calculate. To get an idea, 1AU is around 150.000.000km and 1pc= 1 persec= 3,6 light-year If we talk about Sirius, we have to do this calculations: first of all we have to go from degrees to seconds, 360º=24h->24h=1.440min->1.440min=86.400s. 1AU/2π = 1arc sec/86.400s -> d= 86.400/2π = 43200 AU that is about 6.480.000.000.000km
Cepheid variable star
The cepheid variable star is a star that can variate his brightness. In a graphic with the two variables (Light curve and period), we can see that the entire period of the star is seven days. In this period the star goes from its maximum brightness to its lowest brightness. To arrive at this observation, a lot of data has had to be collected in many years. Also we can see that the nearest stars you can see their movement, but the farhest no. This stars are so important due to his their periodic changes in brightness can be used to figure out how far away they are.