I need an explanation about the below Trigonometric Function, please?

Given that sin u= 5/13 and cos v= -3/5, Both in Quadrant II, find the value of tan(u+v)?
I have already known the answer of the tan(u+v), but I need an explanation about these initial answers from the textbook:
cos u= -sqrt(1-sin²u)= -12/13 and sin v=sqrt(1-cos²v)= 4/5

How does these -12/13 and 4/5 come from?
I checked using calculator according to the given sin u and cos v values, and I got different answers.
Are there a better way to calculate these?

Thank you.

Question

I need an explanation about the below Trigonometric Function, please? 

Given that sin u= 5/13 and cos v= -3/5, Both in Quadrant II, find the value of tan(u+v)?
I have already known the answer of the tan(u+v), but I need an explanation about these initial answers from the textbook: 
cos u= -sqrt(1-sin²u)= -12/13 and sin v=sqrt(1-cos²v)= 4/5

How does these -12/13 and 4/5 come from?
I checked using calculator according to the given sin u and cos v values, and I got different answers.
Are there a better way to calculate these?

Thank you.