I need an explanation about Trigonometric Function, please? Someone from Calculus or higher level should know this.

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 do 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.

I will much appreciate it. Thanks!

Question

I need an explanation about Trigonometric Function, please? Someone from Calculus or higher level should know this.

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 do 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.

I will much appreciate it. Thanks!

amistre64 · Answer

pythag identities, and knowing the values of sin and cos for each quadrant

anonymous · Answer

|dw:1340943042884:dw|
cos u = adjacent/ hyp. = -12/13 [  cos is negative in quad 2 ]
sin v = opp/ hyp = 4/5