Question

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

-225 degrees
-45 degrees
-135 degrees
-405 degrees

Answer 1

225° is not possible

Explanation:

Given that

`\sin \theta=(√(2))/(2)`

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

`\sin \theta=(√(2))/(2)`

`\sin \theta=(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

Answer 2

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.