If sin(pi/2-x) = -4/5 and cos(pi/2-x) = 7/8, what is the exact value of tan x?
I think that I have it but I certainly invite other people to check my logic and working.
sine and cosine are complementary ratios. That is what the co stands for in fronto of the cosine.
Now complemantary angels add up to 90 degrees or pi/2 radians,
sin(pi/2-x) = cos x
cos(pi/2-x) = sin x
cos x = -4/5 = -32/40 It is negative so x must be in the 2nd or 3rd quadrant
sin x = 7/8 = 35/40 It is positive so x must be in the 1st or 2nd quadrant
Hence x must be in the 2nd quadrant.
140317 trig triangle.JPG
From the triangle it can be seen that tan(x)=35/-32
tan(x) = - 35/32
I think that is all okay.