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

In summary, the conversation is discussing how to sketch a unit circle and indicate the range of positions where tanx < or = (-50). The previous problems were easy to solve, but this one is more challenging. The conversation also covers finding the angle between the x-axis and a line with a given slope, as well as shading the appropriate region on the unit circle.
  • #1
UrbanXrisis
1,196
1
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?
 
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  • #2
What is the angle between the x-axis and the line y=mx?
 
  • #3
what's m? how do you find the slope?

is it -88.85 degees
 
  • #4
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.
 
  • #5
m=-50? is that the slope?
 
  • #6
You're not answering my question. Ahh, I'll just give it to you: [itex]\theta[/itex]=arctan(m). Now find the appropriate range of m. And yes, the line y=-50x is involved.
 
  • #7
The inclination of a line is given by:

[tex]\tan \theta = m[/tex], so [tex]\theta = \tan^{-1} m[/tex] as StatusX pointed out. The slope can be found by the equation of the line.
 
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  • #8
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?
 
  • #9
Ok, tan([itex]\theta[/itex]) = 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 [itex]\theta_1[/itex] and [itex]\theta_2[/itex] respectively, with [itex]\theta_2=\theta_1+180^o[/itex]. 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.
 
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  • #10
ohhh okay. I see. So I would shade towards the y-axis right?
 

1. What is a unit circle?

A unit circle is a circle with a radius of 1 unit, centered at the origin (0,0) on a coordinate plane.

2. How do you sketch a unit circle?

To sketch a unit circle, first draw a set of coordinate axes. Then, plot points along the circle at intervals of pi/4 or 45 degrees. Connect these points to form a circle with a radius of 1 unit.

3. What does tanx ≤ (-50) mean?

The notation tanx ≤ (-50) means that the value of tangent of x is less than or equal to -50. This can also be written as -50 ≤ tanx.

4. How do you use a unit circle to find values of tanx ≤ (-50)?

To find values of tanx ≤ (-50) using the unit circle, you can use the coordinates of the points on the circle to determine the tangent ratio. For example, if you draw a line from the origin to the point (-1, -1), the tangent of the angle formed is -1/-1 = 1. This is greater than -50, so it does not satisfy the condition. You can continue to plot points and determine their tangent ratios until you find one that is less than or equal to -50.

5. Why is it important to understand how to sketch a unit circle and find values of tanx ≤ (-50)?

Understanding how to sketch a unit circle and find values of tanx ≤ (-50) is important in many fields of science, such as physics and engineering. It allows you to visualize and solve problems involving angles and trigonometric functions, which are essential in understanding and predicting various phenomena.

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