Solving for theta3

[longhorntt]

Hi,

I'm hoping that I'm doing this right - from the equation below, I'm trying to solve for theta3. Just need a confirmation.

cos^2(theta1) + cos^2(theta2) + cos^2(theta3) = 1

my solution is:

theta3 = arccos(sqrt(1 - (cos(theta1)*cos(theta1)) + (cos(theta2)*cos(theta2)) ))

Thanks!

 

[soroban]

Hello, longhorntt!

I'm hoping that I'm doing this right.

. . \(\displaystyle \text}Solve for }\theta_3\!:\;\;\cos^2\!\theta_1+ \cos^2\!\theta_2 + \cos^2\!\theta_3 \:=\: 1\)

My solution is: .\(\displaystyle \theta_3 \:=\: \arccos\big[\sqrt{1 - \cos^2\!\theta_1 + \cos^2\!\theta_2}\big]\)

Thanks!

Absolutely correct! . . . Good work!

 

[longhorntt]

Thank you soroban! Much appreciated.

 

[srmichael]

Hello, longhorntt!


Absolutely correct! . . . Good work!

Except the plus under the radical should be a minus sign: \(\displaystyle \displaystyle \theta_3=arccos[\sqrt{1-cos^2\theta_1-cos^2\theta_2}]\)

 

[longhorntt]

Yup, you're right - and it was implied in my lame way of writing it out in the OP (code-based).

 

[soroban]

Ha! . . . Missed that! . . . *smack*