Algebra applied to Trigonometry problem

[Moroni]

Homework Statement

tansquaredB=4

solving for B

Homework Equations

This is algebra applied to Trigonometry, through simplification, to arrive at several different answers involving the degrees of angles.

I hope this applies to Physics since physics is "applied Mathematics"

The Attempt at a Solution

B=-tansquared+4

I don't know how to arrive at degrees.

 

[Mark44]

Homework Statement

tansquaredB=4

solving for B

Homework Equations

This is algebra applied to Trigonometry, through simplification, to arrive at several different answers involving the degrees of angles.

I hope this applies to Physics since physics is "applied Mathematics"

The Attempt at a Solution

B=-tansquared+4

With all due respect, your attempt is completely wrong. You are treating "tansquared" is if it had been added on the left side, and have subtracted it from both sides.

Your original equation has nothing to do with addition or subtraction. It is (tan(B))² = 4. It probably appears in your text as tan²B = 4, which is the same as what I wrote earlier.

Your equation is saying that a certain quantity (tan(B)) squared equals 4. What can you do to get rid of the exponent?

I don't know how to arrive at degrees.

 

[Mentallic]

Trigonometry definitely applies to physics. You'll be using it all the time in projectile problems and some other topics.

I recommend you study some trigonometry from a maths textbook.

 

[zgozvrm]

There are 2 answers...

 

[Mentallic]

There are 2 answers...

You'd need to be more specific. There are two equations to solve, essentially $tan(B)=\pm 2$ but there are infinite solutions for B.
But the context of this question is for physics, so there will of course be a restriction on the values of B.

 

[zgozvrm]

You'd need to be more specific. There are two equations to solve, essentially $tan(B)=\pm 2$ but there are infinite solutions for B.
But the context of this question is for physics, so there will of course be a restriction on the values of B.

This is a homework help forum ... I don't want to get too specific.

Unless you consider $$n^\circ$$ and $$(n+360)^\circ$$ to be different angles (which they are not) then there are only 2 answers.

Angles measured in degrees should be represented by the values: [itex]0 \le n < 360[/tex]
Angles measured in radians should be represented by the values: [itex]0 \le n < 2\pi[/tex]
Angles measured in gradians should be represented by the values [itex]0 \le n < 400[/tex]

 

[Mentallic]

Unless you consider $$n^\circ$$ and $$(n+360)^\circ$$ to be different angles (which they are not) then there are only 2 answers.

Physically, yes, but in most mathematics such angles are considered as different solutions. This is why most trigonometry questions are coupled with restrictions as such: (but it is important to be aware that such questions typically have infinite solutions).

Angles measured in degrees should be represented by the values: [itex]0 \le n < 360[/tex]
Angles measured in radians should be represented by the values: [itex]0 \le n < 2\pi[/tex]
Angles measured in gradians should be represented by the values [itex]0 \le n < 400[/tex]

That's fine, but this doesn't support your - still - incorrect statement:

There are 2 answers...

With these restrictions, there are 4 answers.

 

[zgozvrm]

With these restrictions, there are 4 answers.

Yes, you are right ... there are 4 answers!

 

[Mentallic]

Yes, you are right ... there are 4 answers!

 

[Moroni]

Normally I would factor anything with an exponent, to get rid of it.

The problem calls for degrees.

Are 63.43 and 116.57 degrees acceptable solutions?

Thanks!

 

[zgozvrm]

Normally I would factor anything with an exponent, to get rid of it.

The problem calls for degrees.

Are 63.43 and 116.57 degrees acceptable solutions?

Thanks!

That's 2 out of 4!

 

[Mentallic]

Normally I would factor anything with an exponent, to get rid of it.

The problem calls for degrees.

Are 63.43 and 116.57 degrees acceptable solutions?

Thanks!

It depends what the question is asking for. You need to solve $tanB=2$ and $tanB=-2$ so you'd be correct with those solutions, but there are more answers because $tan\theta=tan(\theta+n180^o$ so you could also have 243.43^o and 423.43^o and this goes on infinitely. Is the restriction on the domain $0\leq B < 360^o$ or something similar?

 

[Moroni]

Yes that is the domain like you said.

 

[zgozvrm]

Is the restriction on the domain $0\leq B < 360^o$ or something similar?

Yes that is the domain like you said.

Like I said, there are 4 answers, and you already got 2 of them:

$$63.43^\circ$$ and $$116.57^\circ$$


The other 2 would be:

$$-63.43^\circ = 296.57^\circ$$ and $$-116.57^\circ = 243.43^\circ$$

 

[Moroni]

Thank You both Very Much!