If the value, to the nearest thousandth, of cos θ is -0.385, which of the following could be true about θ?
A. 0 ≤ θ

Question

If the value, to the nearest thousandth, of cos θ is -0.385, which of the following could be true about θ?
A. 0 ≤ θ < π/6
B. π/6 ≤ θ < π/3
C. π/3 ≤ θ < π/2
D. π/2 ≤ θ < 2π/3
E. 2π/3 ≤ θ ≤ π
My ACT Booklet gave me the answer D and an explanation, but I don't understand the explanation at all. Please help.

campbell_st · Answer

ok... so cos is negative... which quadrants are you in..?

goldie1962 · Answer

Well in the fourth quadrant cos is positive, right?

campbell_st · Answer

well your question says 

$$\cos(\theta) = -0.385$$

is that the correct question, or is it

2. 

$$\cos(\theta) = 0.385$$

goldie1962 · Answer

Yes cos(θ) = -0.385

campbell_st · Answer

ok... so which quadrants is cos negative..? that is the key to the question. 

4th and 1st quadrants cos is positive

goldie1962 · Answer

Either second or third I think

goldie1962 · Answer

Okay well I can eliminate A, B, C because they occur in the first quadrant. But doesn't E also fit the bill?

campbell_st · Answer

ok... so the next setp is find the angle 

$$\theta = \cos^{-1}(0.385)$$

then 2nd quadrant angles are 

$$\pi - \theta or 180 - \theta... $$

so you should be able to find the correct solution from there

campbell_st · Answer

so interms of angles measured in degrees 

D is  between 90 and 120

E is between 120 and 180

goldie1962 · Answer

Thank you! I got approx 113 degrees. Why is it π - θ, not 2π/3 - θ?

loser66 · Answer

|dw:1472688217715:dw|

loser66 · Answer

only D or E is the answer. It is D, not E, why? because the beginning of option E is 2pi/3 |dw:1472688318998:dw|