Question

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Answer 1

one sec

Answer 2

tan(x/2) = sin(x) / { 1 + cos(x) } ----- (1)
If sin(x) = 5/13, you can find cos(x) using the identity sin^2(x) + cos^2(x) = 1
and plug sin(x) and cos(x) into (1)

Answer 3

Or try this:
the sine (x) = 5/13
That means sine (x) = opposite / hypotenuse
The length of the third side squared = 13² - 5² = 144
Length of third side = 12
So, tan (x) = 5/12
(Not too sure about solving that for x/2 though.)

Answer 4

In the first quadrant, all trig functions are positive.

Answer 5

sin(x) = 5/13
cos(x) = sqrt( 1 - sin^2(x) )
= sqrt( 1 - 25/169) = sqrt(144/169) = 12/13

tan(x/2) = sin(x) / { 1 + cos(x) }
plug in the numbers.

Answer 6

Yes.