An equation is given Enter your answers as a commaseparated

An equation is given. (Enter your answers as a comma-separated list. Let k be any integer. Round terms to three decimal places where appropriate. If there is no solution, enter NO SOLUTION.) 2 cos(3) = 1

Solution

given

cos(3) = 1

cos(3) = cos(0) or cos(2)

As you know, solutions to cos(x) = 1 are: x = 2 + 2k
Therefore, solutions to cos(3) = 1 are: 3 = 2 + 2k
And so, = (2+2k)/3

= 2(+k)/3

This has values in the interval [0, 2] for k = 0, 1, 2
[when k < 0 we get negative values, when k = 3, we get 8/3 > 2]

k = 0 -----> = (2+2*0)/3 = 2/3
k = 1 -----> = (2+2*1)/3 = 4/3
k = 2 -----> = (2+2*2)/3 = 6/3