1 The sum of the three smallest positive values of theta such that 4(cos*theta)(sin*theta) = 1 is k*pi. Find k?
By the condition of the problem
We can rewrite as
#2costhetasintheta = 1/2#
#sin(2theta) = 1/2#
Now I'm assuming that we're only consider values of
#2theta = pi/6, (5pi)/6, (13pi)/6#
#theta = pi/12, (5pi)/12, (13pi)/12#
Now you just have to add the values up
#theta_"sum" = (19pi)/12#
Hopefully this helps!
The sum of the three smallest positive values of theta