SOLUTION: Suppose cos(u)= 5/13, and sin(u) is negative. Find sin(u-pi), cos(u-pi), sin(u-pi/2), cos(u-pi/2) I tried solving this question but I could not get the right answer. Here are th

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Question 1007348: Suppose cos(u)= 5/13, and sin(u) is negative. Find sin(u-pi), cos(u-pi), sin(u-pi/2), cos(u-pi/2)
I tried solving this question but I could not get the right answer. Here are the step I tried for solving this problem.
cos(u) 5/13 = x/r
Use pythagoream theorem to find sin(u)
x=5, r=13
r^2=x^2+y^2
13^2=5^2+y^2
169=25+y^2
sqrt(144)=y^2 ==> y=12
sin(u)= -12/13
sin(u-pi)
=(-12/13)-(0/1)
=(-12/13)-0 ==> -12/13
cos(u-pi)
=(5/13)-(1/0)
=undefined
sin(u-pi/2)
=(-12/13)-(sqrt(2)/2)
=(-12-sqrt(2))/11
cos(u-pi/2)
=(5/13)-(sqrt(2)/2)
=(5-sqrt(2))/11

Answer by jim_thompson5910(35256) (Show Source):
You can put this solution on YOUR website!
cos(u) = 5/13
sin(u) = -12/13 (found from the pythagorean theorem)
angle u is in quadrant 4

Use this page to look at the identities used. In this case, I'm going to use these two identities

sin(x - y) = sin(x)cos(y) - cos(x)sin(y)
cos(x - y) = cos(x)cos(y) + sin(x)sin(y)

those identities are found in the "Sum and Difference Formulas" section on page 2 of the reference sheet.

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sin(u - pi) = sin(u)cos(pi) - cos(u)sin(pi)
sin(u - pi) = sin(u)(-1) - cos(u)(0)
sin(u - pi) = -sin(u)
sin(u - pi) = -(-12/13)
sin(u - pi) = 12/13

-----------------------------------------------------

cos(u - pi) = cos(u)*cos(pi) + sin(u)*sin(pi)
cos(u - pi) = cos(u)*(-1) + sin(u)*0
cos(u - pi) = -cos(u)
cos(u - pi) = -5/13

-----------------------------------------------------

sin(u - pi/2) = sin(u)cos(pi/2) - cos(u)sin(pi/2)
sin(u - pi/2) = sin(u)(0) - cos(u)(1)
sin(u - pi/2) = -cos(u)
sin(u - pi/2) = -5/13

-----------------------------------------------------

cos(u - pi/2) = cos(u)*cos(pi/2) + sin(u)*sin(pi/2)
cos(u - pi/2) = cos(u)*(0) + sin(u)*1
cos(u - pi/2) = sin(u)
cos(u - pi/2) = -12/13