Sketching a Unit Circle: Finding tanx ≤ (-50)

[UrbanXrisis]

Question:

sketch a unit circle and indicate the range of positions where tanx < or = (-50).

I have no clue how to do this. THe previous problems in my homework were easy, such as: sketch a unit circle and mark two positions where sin = 1/3 or -1/3. I would just move up 1/3 on the y and go over to where the circle is and put a dot. I could also go down 1/3 on the y and go over to where the unit circle is and put a dot. but how would I do tanx<= -50?

 

[StatusX]

What is the angle between the x-axis and the line y=mx?

 

[UrbanXrisis]

what's m? how do you find the slope?

is it -88.85 degees

 

[StatusX]

I mean, for some slope m, what is the angle, in terms of m? (it involves arctan). You don't need a calculator for this question.

 

[UrbanXrisis]

m=-50? is that the slope?

 

[StatusX]

You're not answering my question. Ahh, I'll just give it to you: $\theta$=arctan(m). Now find the appropriate range of m. And yes, the line y=-50x is involved.

 

[z-component]

The inclination of a line is given by:

$$\tan \theta = m$$, so $$\theta = \tan^{-1} m$$ as StatusX pointed out. The slope can be found by the equation of the line.

 

[UrbanXrisis]

theta is -88.85 degees. do I'm not sure where I shade. from the x-axis to the -88.85 degees or form the y-axis to the -88.85 degees?

 

[StatusX]

Ok, tan($\theta$) = y/x, right? Now, picture a line through the origin defined by y=mx. You can think of this line as two rays coming out of the origin in opposite directions. Each ray makes a certain angle with the x-axis, which we'll call $\theta_1$ and $\theta_2$ respectively, with $\theta_2=\theta_1+180^o$. Now, for every point on the line, y/x=m. So the tan of both these angles is m. Do you see that? If so, now you know which rays coming out of the origin correspond to the region you need to shade.

 

[UrbanXrisis]

ohhh okay. I see. So I would shade towards the y-axis right?