Solve cos x = -2/3 for 0 ≤ x < 2π (round to the nearest hundredth of a radian).

Question

Having trouble with this problem, have tried solving but receive the wrong answer multiple times. Solve cos x = -2/3 for 0 ≤ x < 2π (round to the nearest hundredth of a radian). Thank you!

Answer 1

In every trig question - draw the unit circle. I can't do it here - but if you contact me for a free 10 minutes lesson - I will show it in detail

X = cos^-1(-2/3) = 2.3 rad (a bit less then pi) which is in the II quarter (where cos is negative)

There is also a second symmetrical solution in the III quarter (where cos i negative as well)

X = -2.3 rad

But since you need angle in 0 ≤ x < 2π - add 2pi (to get co-terminal angle in the required diapason):

X = -2.3 + 2*pi = 3.983 rad (a bit more then pi)

Answer 2

A negative cosine means the angle is in either the 2nd or 3rd quadrant, where x is negative.

With a cosine of 2/3, the basic angle is 0.841 radians (+ or -)

Since we have -2/3, the angle is pi ± 0.841

If this is not what you are being given, then tell us what it's supposed to be, and we can maybe figure out the disconnect.