Use the figure below, which shows the unit circle with increments of 0.1 units marked off along the circumference in a counterclockwise direction starting from (1, 0).

Estimate θ if
cos θ = −0.6
and 0 ≤ θ

Question

Use the figure below, which shows the unit circle with increments of 0.1 units marked off along the circumference in a counterclockwise direction starting from (1, 0).

Estimate θ if 
cos θ = −0.6
 and 0 ≤ θ < 2π. (Enter your answers as a comma-separated list. Round your answers to one decimal place.)
θ =___

liziekay · Answer

attachment

3mar · Answer

May I help?

liziekay · Answer

Yes! @3mar

3mar · Answer

The idea is in the definition of cos:
$$\cos \theta=\frac{ adj }{ hyp }$$
and because the cosine is negative (-0.6), that means theta is in either the second or third quadrant.

3mar · Answer

Do you follow?

3mar · Answer

Excuse me.
I am busy and due to your lake of response, I am going to leave.
Salam.

liziekay · Answer

Sorry, I didn't see your response..

liziekay · Answer

Yes, I follow. Exactly what I thought

3mar · Answer

So what is the next step do you think?

liziekay · Answer

The next step would be to plug in values for cos. What would be the adjacent and hypotnuse.

3mar · Answer

and the hyp is always 1 (unit circle with unity radius)
then where will you plot -0.6?

liziekay · Answer

In a quadrant..

liziekay · Answer

so -.6/1 for cos theta

3mar · Answer

As we all know, cos is negative in II and III. ok?

3mar · Answer

"In a quadrant.."???

liziekay · Answer

It depends on if x is -.6 o if y is -.6...

liziekay · Answer

I believe it would be in the third quadrant since it's negative

liziekay · Answer

so cos is .9999451694

3mar · Answer

and II also.....why not?
Is not cos(140)= -ve (for example)?

liziekay · Answer

that's a possibility

liziekay · Answer

is cos t=x and sin t= y going to help in this case?

3mar · Answer

We do all what we know, he did not put a restriction about theta, rather he said
$$0<\theta<2\pi$$
so every quadrant theta is negative, we accepted.

liziekay · Answer

Ok, so are we plugging in the values of cos theta into the statement mentioned above?

liziekay · Answer

cos is .6 divided by 1

3mar · Answer

$$\cos \theta=\frac{ -0.6 }{ 1 }=-0.6$$

liziekay · Answer

but cos of (-.6/1) turns out on a calculator as .9999451694

liziekay · Answer

Is that going to help us in any way?

3mar · Answer

Please we are now in the graph, don't disturb yourself with the calculator results.

liziekay · Answer

Ok

3mar · Answer

Take that pic, please. It would clear a lot.

liziekay · Answer

I see how you got that

3mar · Answer

Look at the fugure and tell me where the hypotenuse touches the circle in quadrant II and III?

liziekay · Answer

the hypotenuse touches 2.2 and about 4.1

liziekay · Answer

wow, that was quite simple....... I must have not been thinking....... Thank you for spending the past hour helping me (:

3mar · Answer

Yes, 2.2 and 4.1 (actually it is before 4.1 a little bit, but anyway...)

liziekay · Answer

Would you be available to help with one more?

3mar · Answer

Even the past day, I will never be late for any help any time.

What you just wrote "the hypotenuse touches 2.2 and about 4.1" is the answer required and you are looking for, simply.

Don't distract yourself.

Be at the top always.

liziekay · Answer

Okay! Thank you! I'm not understanding what I'm doing wrong in this problem, let me post a picture of the problem itself.

3mar · Answer

Ok.

3mar · Answer

You need " help with one more" now?

liziekay · Answer

yeah.. Could you help?

liziekay · Answer

attachment

liziekay · Answer

|dw:1475086241112:dw|

liziekay · Answer

|dw:1475086313361:dw|

liziekay · Answer

|dw:1475086338561:dw|

liziekay · Answer

|dw:1475086366570:dw|

liziekay · Answer

20 divided by three is 6.666667 and that times four is 26.6666667

liziekay · Answer

26.66 is incorrect....

3mar · Answer

Really and so busy, can I go now and come back to discuss it after 100 min?