Angle Between Two Vectors: Solving for θ

[nabelekt]

Homework Statement

Vectors and have scalar product -7.00 and their vector product has magnitude 3.00.
What is the angle between these two vectors?

Homework Equations

|A| |B| cosθ = -7
|A| |B| sinθ = 3

The Attempt at a Solution

tanθ = (-3/7)
tan^-1(-3/7)=θ

When I enter tan^-1(-3/7) into my calculator, I get -23.199, but when I enter 23.199 into MasteringPhysics, it tells me that I am incorrect. What am I doing wrong?

Thanks!

 

[voko]

Is the angle expected in degrees or radians?

 

[nabelekt]

The answer is required to be in degrees.

 

[voko]

What is the range of arctan? From the given values, can you determine whether the angle is really in that range?

 

[nabelekt]

I believe that the range of arctan is 270°<θ<90°. Correct? 23.199° seems to be in that range…

Thanks for the help. It's been a while since I've done this stuff.

 

[CAF123]

The range given does not make sense. The range should be (-π/2,π/2).

 

[voko]

http://en.wikipedia.org/wiki/Inverse_trigonometric_functions

That's about the range of arctan.

Now think, in what quadrant does the angle really lie?

 

[nabelekt]

I guess it would actually lie in quadrant II whereas the range of arctan is quadrants I and IV. So what should I do?

 

[voko]

You should express you angle via some auxiliary angle that is in the range of arctan, obtain the value of the auxiliary angle, and then get your angle.

 

[gabbagabbahey]

Homework Statement

Vectors and have scalar product -7.00 and their vector product has magnitude 3.00.
What is the angle between these two vectors?

Homework Equations

|A| |B| cosθ = -7
|A| |B| sinθ = 3

The Attempt at a Solution

tanθ = (-3/7)
tan^-1(-3/7)=θ

When I enter tan^-1(-3/7) into my calculator, I get -23.199, but when I enter 23.199 into MasteringPhysics, it tells me that I am incorrect. What am I doing wrong?

Thanks!

You should take care to notice two things here:

(1) If |A| |B| cosθ = -7, then cosθ must be negative. In which quadrants is cosθ negative?

(2) tanθ has a period of ∏ radians, so tanθ = tan(θ+n∏) for any integer n, and tan^-1(tanθ) = θ +n∏. Can you find a value of n that gives you an angle in the correct quadrant for θ +n∏=tan^-1(-3/7)?