I need help please solving this equation

[Geophysics 111]

Greeting All,
Can you please help me in this problem. I need to solve for Ax. The equation is:
D=atan((sqrt(Ax*Ax+Ay*Ay)/Az))
I need Ax=..........
Can you please help me?

 

[Dr.Peterson]

Start by taking the tangent of each side, then either square each side or multiply by A_z.

Please show any work you have done, so we can help you move on from there.

 

[Geophysics 111]

Thanks.
What I got is
tan D*Az= sqrt(Ax*Ax+Ay*Ay)
Then
tan (D*Az)^2 = Ax*Ax +Ay*Ay
Ax*Ax=tan (D*Az) ^2 - Ay*Ay
Is this write? I want only Ax

 

[Deleted member 4993]

Thanks.
What I got is
tan D*Az= sqrt(Ax*Ax+Ay*Ay)
Then
tan (D*Az)^2 = Ax*Ax +Ay*Ay
Ax*Ax=tan (D*Az) ^2 - Ay*Ay ............................ Correct
Is this write? I want only Ax

You have only Ax on the left-hand-side of the equation!

 

[Geophysics 111]

Thanks.
So I will take sqrt for both sides to get one Ax.

 

[Dr.Peterson]

Correct except that you put D inside the parentheses, which is wrong.

You should have said this:

D = atan(sqrt(Ax*Ax+Ay*Ay)/Az)​

tan(D) = sqrt(Ax*Ax+Ay*Ay)/Az​

Az*tan(D) = sqrt(Ax*Ax+Ay*Ay)​

(Az*tan(D))^2 = Ax*Ax+Ay*Ay​

(Az*tan(D))^2-Ay*Ay = Ax*Ax​

So the result is Ax = sqrt((Az*tan(D))^2 - Ay*Ay).

 

[Geophysics 111]

Correct except that you put D inside the parentheses, which is wrong.

You should have said this:

D = atan(sqrt(Ax*Ax+Ay*Ay)/Az)​

tan(D) = sqrt(Ax*Ax+Ay*Ay)/Az​

Az*tan(D) = sqrt(Ax*Ax+Ay*Ay)​

(Az*tan(D))^2 = Ax*Ax+Ay*Ay​

(Az*tan(D))^2-Ay*Ay = Ax*Ax​

So the result is Ax = sqrt((Az*tan(D))^2 - Ay*Ay).

Thanks a lot

 

[Steven G]

Thanks.
What I got is
tan D*Az= sqrt(Ax*Ax+Ay*Ay)
Then
tan (D*Az)^2 = Ax*Ax +Ay*Ay
Ax*Ax=tan (D*Az) ^2 - Ay*Ay
Is this write? I want only Ax

No, it is not correct.
Note that tan(r)*s \(\displaystyle \neq\)tan(rs). That is tan D*Az \(\displaystyle \neq\)tan (D*Az).
Also if you want to square tan (D*Az) you do not get tan[(D*Az)²], rather you get [tan(D*Az)]² more commonly written as tan²(D*Az)

Also your answer must be wrong since you solved for Ax*Ax when you wanted to solve for Ax!

 

[Steven G]

You have only Ax on the left-hand-side of the equation!

Do you want to reconsider that?

 

[Deleted member 4993]

Do you want to reconsider that?

No..... there is NO other Variable on the right hand side.

I did not declare that the answer has been found!

 

[Steven G]

You have only Ax on the left-hand-side of the equation!

It looks to me that the OP has Ax*Ax on the lhs, not Ax. What am I missing?

 

[Deleted member 4993]

It looks to me that the OP has Ax*Ax on the lhs, not Ax. What am I missing?

I wanted OP to discover that one more step is needed.