Find all possible values for cos(theta) = -1/2.

When I plugged arccos(-1/2) = 2pi/3.

However, on the book it says that there are two solutions, 2pi/3 and 4pi/3. Can someone please explain to me how did they get the other number?

Question

Find all possible values for cos(theta) = -1/2.

When I plugged arccos(-1/2) = 2pi/3.

However, on the book it says that there are two solutions, 2pi/3 and 4pi/3. Can someone please explain to me how did they get the other number?

anonymous · Answer

@satellite73

anonymous · Answer

@tkhunny

anonymous · Answer

@AccessDenied

anonymous · Answer

@iPwnBunnies

ipwnbunnies · Answer

Do you know which quadrants cosine is negative?

anonymous · Answer

Look at the unit circle. 2pi/3 is 120 degree. And 4pi/3 is 240 degree.

ipwnbunnies · Answer

|dw:1398136665149:dw|
All functions are positive in Q1
Sine is + in Q2
Tan in Q3
Cos in Q4

anonymous · Answer

I know, but I want a mechanical method like an equation or something.

ipwnbunnies · Answer

It's not really an equation. It's just one of those patterns you have to recognize.

anonymous · Answer

Because I am currently in calculus II and I am doing applications with these.

ipwnbunnies · Answer

We know pi/3 has a cosine of 1/2, as stated.
So similar angles will have a numerical value of 1/2, but it may be positive or negative.

ipwnbunnies · Answer

Ok.