Question

find all solutions to the equation
cos x = -1/2

Answer 1

Hint: the cosine is negative in the second and third quadrants. and the angle whose cosine is 1/2 is pi/3 radians.

Answer 2

i don't know how to solve it

Answer 3

pi/3 is in the first quadrant though

Answer 4

yes - but from this you should find the 2 angles in the second and third quadrants.

Answer 5

angle in 2nd quadrant = pi - pi/3 = 2pi/3

Answer 6

so are the other solutions 4pi/3 and 5pi/3?

Answer 7

there is only one more solution - the one in 3rd quadrant

Answer 8

pi + pi/3

Answer 9

so its 4pi/3

Answer 10

Yes
I am assuming the question only wants solutions in the range 0 to 2pi

Answer 11

yes

Answer 12

OK so these are your 2 solutions
2pi/3 , 4pi/3
or 120 , 240 degrees

Answer 13

is this answer choice correct
\[\left\{ \frac{ 2\pi }{ 3 } + 2n \pi, \frac{ 4\pi }{ 3 }+ 2n \pi n= 0, +/-1, +/-2,...\right\}\]