Question

If sin theta = sqrt(2/2), which could not be the value of theta?

Answer 1

The solution would be like this for this specific problem:

sin(θ°) = √(2)/2 

θ° = 360°n + sin⁻¹(√(2)/2) and θ° = 360°n + 180° − sin⁻¹(√(2)/2)
θ° = 360°n + 45° and θ° = 360°n + 135° where n∈ℤ 

360°*0 + 45° = 45° 
360°*0 + 135° = 135° 
360°*1 + 45° = 405° 

sin(225°) = -√(2)/2

225 has an angle where sin theta= -(sqrt2)/2 therefore, the value of theta cannot be 225 degrees.

Answer 2

Answer:

225° is not possible

Step-by-step explanation:

Given that

$\sin \theta=\frac{\sqrt{2}}{2}$

we have to choose the option which could not be the value of theta.

$\sin \theta=\frac{\sqrt{2}}{2}$

$\sin \theta=\frac{1}{\sqrt2}=\sin45^{\circ}$

$\theta=45^{\circ}$

As sine is positive in second and fourth quadrant.

⇒ $\sin 45=\sin(180-45)=\sin135$

Also, $\sin 45=\sin(360+45)=\sin405$

$\text{Hence, the value of }\theta \text{which are possible are } 45^{\circ}, 135^{\circ}, 405^{\circ}$

Therefore 225° is not possible