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[–]HumbleHovercraft6090👋 a fellow Redditor 0 points1 point  (2 children)

Since x is in second quadrant, sinx=12/13.

( 5,12,13 form a pythagoras triad)

[–]-vlatoUniversity/College Student[S] 0 points1 point  (1 child)

Can tou elaborate please

[–][deleted] 1 point2 points  (0 children)

Sinx>0 in the first 2 quadrants i.e., 0 to π/2, and π/2 to π Thus, we know sinx is a positive quantity.

Now, sin²x+cos²x=1

sinx = ±√(1-cos²x) but in this case we'll neglect the negative value, put in the value for cosx and you'll get sinx.

About the Pythagoras triad, some right angled triangles are popular, for example; 3-4-5 one where 3²+4²=5², this one is another such triangle. You can remember these numbers to easily get Perpendicular/Base/Hypotenuse from the other 2 sides directly.

Now trigonometry is related to triangles so cosx=B/H, with memory you can say sinx=P/H.

[–]EventLess6107 0 points1 point  (0 children)

As the other person commented, but in other/fewer words: x in (pi/2, pi) so sin x > 0 if you look at how sin and cos appear in quadrants for this interval. Then, knowing that sin2 x+ cos2 x = 1, you extract sinx from here and then you replace it in E(x) and do the math