Question

What is the maximum value of sin24+cos7?

Answer 1

2

Answer 2

sin 24<sin 30=1/2
cos 7<cos 0=1
sum<3/2

Answer 3

Generally, the max of sin(x) + cos(x) shouldn't exceed 2. This is impossible though since there is no value in which both sinx and cosx equals 1. However, if you notice, from 0 to 90 (degrees), sinx increases. In that same interval, cosx decreases. That means:

We can round sin 24 to sin 30 because sin30 > sin 24 and round cos 7 down to cos 0 because cos 0 > cos 7.

cos 0 = 1. sin 30 = 1/2.
Max = 3/2