Question

Find all t that satisfy cos(t)=-1/2 for t belongs to [0,3pi]

Answer 1

In which quadrants is cosine negative?

Answer 2

Is it II and IV?

Answer 3

It is II and III

Answer 4

cos(pi/3) = 1/2. So the reference angle is pi/3.
Since cosine is negative in quadrant II and III, the angles are:
pi - pi/3, pi + pi/3, for angles in [0,2pi].
Simplify the angles first and then we will get to [0,3pi].

Answer 5

2pi/3 and 4pi/3?

Answer 6

correct.
Now 3pi = 2pi + pi.
So we need one more angle that falls in the second quadrant.
Out of 2pi/3 and 4pi/3, 2pi/3 is in the second quadrant to which if we add a 2pi it will make one full rotation and come back to quadrant II.
2pi/3 + 2pi = 2pi(1/3 + 1) = 2pi * 4/3 = 8pi/3.

Therefore, in the interval [0, 3pi], the angles are 2pi/3, 4pi/3, 8pi/3

Answer 7

I see! Thank you so much!!!

Answer 8

You are welcome. The above answers in radians is the correct way to answer it.

But for ease of understanding, the angles in degrees are: 120, 240, 480.