Question

What is the maximum integer value of n, where n<148,
that satisfies the following inequalities: sin(pi/2+(pi*n)/74)<0 and tan(pi−(pi*n)/74)<0?

Answer 1

sin(π/2+(nπ)/74) < 0
cos(nπ/74) < 0
cos(x) < 0 in QII,QIII, so
cos 148π/74 = cos2π >= 0
Since 3π/2 is 3/4 (2π),
n < 3/4 (148)
n < 111

figure out a similar range for n where tan < 0 (QII,QIV)

pick the largest value of n. I figure it will be in QII, since we must have tan and cos both < 0.

Answer 2

So it would be 110 ? or which n is in QII