I was doing some SAT practice problems and I came upon this math question
It is given that cos(k)=j where k is the radian measure of an angle and pi<k<3pi/2. If cos(h)=-j, which of the following could be the value of h?
a) 3pi-k
b) k-2pi
c) k+2pi
d) k+3pi
I know why b and c are incorrect and when I first solved the problem, I got (d) as the correct answer, which is what is listed in the answer book. I was trying to figure out why (a) can be eliminated. I plugged in values to (a) and they were satisfying the conditions for me.
Ex. if k=5pi/4 then j= -sqrt2/2 therefore cos(h) has to be +sqrt2/2. If you subtract 5pi/4 from 3pi, you get 7pi/4 as h,and cos(7pi/4) is +sqrt2/2.
if k=7pi/6, j= -sqrt3/2. Subtracting 7pi/6 from 3pi gives you 11pi/6 as h and cos(h)= +sqrt3/2
Since k is restricted to quadrant 3, when you subtract k from 3pi, it ends up in quadrant 4, where cos is positive and the opposite of cos in q3, satisfying the condition.
Can anyone tell me what I am doing wrong and why (a) is incorrect?
