Calculator inverse tangent problem

In summary, the problem involves a pilot steering a plane with a given wind direction and speed. To find the true course and ground speed of the plane, the resultant vector must be calculated using trigonometry. The resultant vector is in the second quadrant and the angle can be found using the inverse tangent function. However, if the resultant vector is in the second quadrant, the calculated angle may be incorrect. It is necessary to use trig identities, specifically the identity for tangent of a sum, to find the correct angle.
  • #1
merced
44
1

Homework Statement


Suppose that a wind is blowing from the direction N45ºW at a speed of 50 km/h. A pilot is steering a plane in the direction N60ºE at an airspeed of 250 km/h. Find the true course (direction) and ground speed (magnitude) of the plane.

Homework Equations



The Attempt at a Solution



The resultant vector will be in an upward direction in the second quadrant, right? I determined that the resultant vector
v = <25(√2) - 125(√3), 25(√2) + 125>

I am trying to find the angle that the plane is flying.
tan θ = [25(√2) + 125]/[25(√2) - 125(√3)]
Using inverse tangent and my calculator, I got an angle around -41.5 degrees.
If the resultant vector is in the second quadrant, this is wrong. I remember that the calculator sometimes will not work for inverse tangent, but I can't remember when, or what to do to fix it.

Please help.
 
Physics news on Phys.org
  • #2
Use your trig identities. What is [itex]\tan(\theta+180^\circ)[/itex]?
 
  • #3
The same thing...I was thinking I had to add something. I couldn't remember what though. Thanks
 

1. What is the inverse tangent function on a calculator?

The inverse tangent function, also known as arctangent, is a mathematical function that calculates the angle whose tangent is a given number. It is often denoted as tan-1 or atan, and it is the inverse of the tangent function.

2. How do I access the inverse tangent function on a calculator?

The inverse tangent function is usually found as a secondary function on calculators, meaning you have to press the "2nd" or "shift" button before pressing the tangent button. On some calculators, it may also be labeled as "tan-1" or "atan".

3. Can I use the inverse tangent function to find the angle of a right triangle?

Yes, the inverse tangent function can be used to find the angle of a right triangle. Simply input the ratio of the triangle's opposite side to its adjacent side (opposite/adjacent) into the calculator and take the inverse tangent of that number to find the angle in radians. If you want the angle in degrees, you can multiply the result by 180/π.

4. Are there any special considerations when using the inverse tangent function on a calculator?

Yes, when using the inverse tangent function, it is important to make sure your calculator is in the correct mode (degrees or radians) and that you are using the correct input (opposite/adjacent or y/x). Additionally, the inverse tangent function is only defined for certain values, so make sure your input falls within the appropriate range.

5. Can the inverse tangent function be used to solve other types of problems?

Yes, the inverse tangent function can be used to solve a variety of problems, including finding the angle between two vectors or the slope of a curve at a given point. It is also an important tool in calculus for solving integrals and differential equations.

Similar threads

  • Calculus and Beyond Homework Help
Replies
9
Views
2K
  • Calculus and Beyond Homework Help
Replies
8
Views
300
  • Calculus and Beyond Homework Help
Replies
2
Views
3K
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
8
Views
1K
  • Calculus and Beyond Homework Help
Replies
2
Views
7K
  • Calculus and Beyond Homework Help
Replies
1
Views
2K
  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Introductory Physics Homework Help
Replies
2
Views
2K
  • Calculus and Beyond Homework Help
Replies
4
Views
1K
Back
Top