Trig Problem, where am I going wrong?
Hello everyone, I'm new to these forums. The long story short is I am trying to finish high school via correspondence, and I need to do two math courses, each containing four units. I am on the fourth unit, the first three gave me very few problems. Anyways, here is the problem:
2cos^2x+cosx=0 Solve for the domain (0, 2pi) to nearest hundredth of a radian.
I did this:
x=1.57 (this is pi/2 or 90degrees)
Therefor for the first zero, x=1.57, 4.71
For the second zero:
x=2.09 (this is 2pi/3 or 120degrees)
CAST RULE: since cosx is negative, the angle is in quadrants two and three:
So we have 1.57, 4.71, 1.05, 5.23
However when I check my answer on mathway, it shows the solutions as:
I don't understand why my calculations for the second zero are wrong. If I use quadrants ONE and FOUR (where cosx should be positive), I get 2.09 and 4.19, which is what mathway shows as the correct answers.
Can someone tell me where I'm going wrong here? The second zero calculates to cosx=(-1/2), and cosx is negative in quadrants two and three, not one and four ... I don't see my error.