Question

Which shows all the exact solutions of

Which shows all the exact solutions of
θ ²=0? Give your answer in radians.

Options:
Option 1: θ=0
Option 2: θ=π
Option 3: θ=2π
Option 4: θ=nπ

Answer 1

The exact solutions of θ ² = 0 in radians are found only when θ = 0. The other options are incorrect because squaring π or any multiple of π does not result in 0. Option 1: θ = 0 is the correct choice.

Step-by-step explanation:

The question 'Which shows all the exact solutions of θ ² = 0?' asks us to find all the values of θ that satisfy the given equation. We are given four options, and we need to determine which represents the correct solutions in radians.

Solution:

• The equation θ ² = 0 has one obvious solution: when θ = 0. This is because 0 squared is equal to 0.
• Looking at the other options: θ = π, θ = 2π, and θ = nπ, we can determine that none of these other options are correct because if you square π or any multiple of π, you will not get 0.
• Therefore, the only value of θ that satisfies the equation is θ = 0. This means that Option 1: θ =0 is the correct choice.

To check the answer, we can square θ = 0 to see that it indeed equals 0, which confirms that our solution is reasonable.