Question

at which of the following values is sin θ negative? (1 point) ○ sin θ = 90° ○ sin θ = 0° ○ sin θ = 270° ○ sin θ = 120°

Explanation:

Step1: Recall sine values of standard angles

We know the sine values for some standard angles:

• $\sin 90^\circ = 1$ (positive)
• $\sin 0^\circ = 0$ (neither positive nor negative)
• $\sin 270^\circ = - 1$ (negative)
• $\sin 120^\circ=\sin(180^\circ - 60^\circ)=\sin60^\circ=\frac{\sqrt{3}}{2}$ (positive)

Step2: Identify the angle with negative sine

From the above calculations, we can see that among the given options, $\sin270^\circ$ is negative.

Answer:

$\sin\theta = 270^\circ$ (or the option corresponding to $270^\circ$)