Need help on how they got these numbers -- solution to a trig equation

[AzureSekki]

Summary:: This is not a homework i just need clarification on how they got those number
Any solution involving sine and cosine is my weakness when its advance or intermediate

 

[fresh_42]

Do you know how to solve $ax^2+bx+c=0$?

... and it does belong into our homework forums, whether it is or not.

 

[HallsofIvy]

Let $$x= sin(\theta)$$. Then $$9sin^2(\theta)- 5.4326sin(\theta)+ 1.4602= 0$$ becomes $$9x^2- 5.4326x+ 1.4602= 0$$. Solve for x by "completing the square" or using the quadratic formula.

However, this equation has only complex roots so will not give the values of $$\theta$$ you have. Are you sure you have copied it correctly?

 

[AzureSekki]

Thank you

 

[SammyS]

Summary:: This is not a homework i just need clarification on how they got those number
Any solution involving sine and cosine is my weakness when its advance or intermediate

View attachment 257521

It's generally recommended that type the problem statement.

It seems that the problem you wrote and then photographed is:
$4\sin^2(\theta)- 5.4326\sin(\theta)+ 1.4602= 0$

It's difficult to see that the first coefficient is a 4 and not a 9 .