Question

Solve the equation 3+sin theta=frac{6-sqrt{2}}{2}

Trigonometric equation and identitie
ANSWERED
asked 2020-11-11
Solve the equation \(3+\sin \theta=\frac{6-\sqrt{2}}{2}\)

Answers (1)

2020-11-12

Separate the right side
\(3+\sin \theta= 3-\frac{\sqrt{2}}{2}\)
Substruct 3 from both sides
\(\sin \theta= -\frac{\sqrt{2}}{2}\)
The reference angle is \(\theta'=45°\) since \(45°=\frac{\sqrt{2}}{2}\). Recall that sine is negative on QIII and QIV.
The QIII solution is
\(\theta=180°+\theta'=180°+45°\)
\(\theta=225°\)
The QIV solution is
\(\theta=360°-\theta'=360°-45°\)
\(\theta=315\)°

0
 
Best answer

expert advice

Have a similar question?
We can deal with it in 3 hours
...