Question

find all angles, 0° ≤ θ < 360°, that solve the following equation. cosθ = 0 answer additional solution no solution θ = | ° submit answer

Explanation:

Step1: Recall cosine values

We know that $\cos\theta = 0$ when $\theta$ is $90^\circ$ or $270^\circ$ in the range $0^\circ \leq \theta < 360^\circ$. This is from the unit circle, where the x - coordinate (which represents $\cos\theta$) is 0 at $\frac{\pi}{2}$ (or $90^\circ$) and $\frac{3\pi}{2}$ (or $270^\circ$) radians (or degrees in this case).

Step2: List the solutions

So the angles $\theta$ that satisfy $\cos\theta = 0$ with $0^\circ \leq \theta < 360^\circ$ are $90^\circ$ and $270^\circ$. Since the problem might be expecting all solutions, we need to present both. But if we consider the input box, maybe we can list them. However, the equation $\cos\theta = 0$ has two solutions in the given interval.

Answer:

The angles are $90^\circ$ and $270^\circ$. So $\theta = 90^\circ, 270^\circ$