Question

Without using a calculator, find all solutions to cos(theta) = -sqrt(2)/2 in the interval 0 <=theta<= 2pi. If there is more than one answer, enter your answers as a comma separated list. Your answers should be exact values (given as fractions, not decimal approximations).

Answer 1

Are we allowed to assume knowledge of the 'basic' trig values - i.e. 0, pi/6, pi/4, pi/3, pi/2 ?

Answer 2

yeah

Answer 3

cos(pi/4) = sqrt(2)/2 (if we can;t assume, that can be proved with a simple triangle).

cos(pi-x) = -cos(x) => cos(pi-pi/4) = cos(3pi/4) = -sqrt(2)/2
cos(2pi-x) = cos(x), so 2pi/3pi/4 = 5/4pi is also a solution

Answer 4

Oh, you're not going to thank me? *awkward*

Answer 5

haha sorry I was working on my other problems...thanks