Question

For how many values of theta such that 0<theta<360 do we have cos theta = 0.1? (Note that theta is a measure in radians, not degrees!)

I'm kinda confused with the problem? Could someone help me? I'm thinking unit circle, so cos is the x coordinate. It would be easy if theta = degrees, but it is radians, so I'm confused?
IF it were degrees, it would be 2 right.

Answer 1

degrees or radians or grads, it's still 2. What you call the angle does not matter.

If you plan to succeed in trig, get used to thinking in radians. Once you get past the introductory material, most problems will deal with radians.

Answer 2

Thank you sir, I will take your advice.
However, this problem is for an online class, and 2 does not seem to be the answer. Hmm...why?

Answer 3

cos x is positive in QI,QIV.
There's only one angle in each quadrant where cos x = 0.1

Answer key is wrong, if your question is correct.

Answer 4

Wait, is cos x the y coordinate or the x coordinate?

Answer 5

doesn't matter. All of the trig functions are positive in exactly 2 of the 4 quadrants.

Answer 6

Well think about it. The period of cos(x) is 2pi, 114pi = 358.14, so cos(x) repeats 114/2 = 57 times. So the answer is 57*2 = 144, but since cosine is split over y axis on the first period (calculatorsoup dot com/images/trig_plots/graph_cos_pi.gif)
we add 1 to 144, and get 145.