If sin(u)=12/13 and cos(u) is negative?

Question

cos(u) = -5/13
tan(u) = 12/-5
sin(-u) = -12/13
cos(-u) = 5/13
tan(-u) = 12/5
sin(u+pi) = -12/13
cos(u+pi) = 5/13
tan(u+pi) = -12/5
sin(u+(pi/2)) = -5/13
cos(u+(pi/2)) = -12/13
tan(u+(pi/2)) = 5/12

 

these are my answers Im being told that im incorrect, however Im not being told which one(s) is incorrect. Im racking my brain to try and figure this out.

 

Answer 1

Hi Skylar!

 

I hope I'm not too late to help.  The easiest way for me to do these problems is to draw (yes draw it) a right triangle and label one of the smaller angles u.  The hypotenuse is 13 and the side opposite u is 12.  Don't worry about drawing it to scale.  This is just scratch work.  Using the Pythagorean Theorem, we can find that the last side is 5.  (I can see that you know this.)  Now, beside the triangle, draw small x and y axes.  Since the sine is positive and the cosine is negative, u is in the 2nd quadrant.  So write a u somewhere in that space as a memory jogger.  That way, you can think u +π is in the opposite quadrant i.e. 4th quadrant.  To find the angle -u, go back to the origin and think backwards to see that -u is in the 3rd quadrant.  I hope this helps!

 

Lori