Question

the point \\(p(x, y)\\) lies on the terminal side of an angle \\(\theta = \frac{3\pi}{4}\\) in standard position. what are the signs of the values of \\(x\\) and \\(y\\)?

both \\(x\\) and \\(y\\) are positive.
both \\(x\\) and \\(y\\) are negative.
\\(x\\) is positive, and \\(y\\) is negative.
\\(x\\) is negative, and \\(y\\) is positive.

Explanation:

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<reasoning>

Determine the quadrant of the angle

\[
\frac{\pi}{2} < \frac{3\pi}{4} < \pi
\]

Identify the signs of coordinates in Quadrant II

\[

$$\begin{aligned} x &< 0 \\ y &> 0 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>Both x and y are positive.</mcq-option>
<mcq-option>Both x and y are negative.</mcq-option>
<mcq-option>x is positive, and y is negative.</mcq-option>
<mcq-correct>x is negative, and y is positive.</mcq-correct>
</answer>

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"properties": {
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{
"type": "point",
"params": [[-2.12, 2.12]],
"properties": {
"name": "P(x, y)",
"color": "#F2557F",
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Answer:

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<reasoning>

Determine the quadrant of the angle

\[
\frac{\pi}{2} < \frac{3\pi}{4} < \pi
\]

Identify the signs of coordinates in Quadrant II

\[

$$\begin{aligned} x &< 0 \\ y &> 0 \end{aligned}$$

\]
</reasoning>

<answer>
<mcq-option>Both x and y are positive.</mcq-option>
<mcq-option>Both x and y are negative.</mcq-option>
<mcq-option>x is positive, and y is negative.</mcq-option>
<mcq-correct>x is negative, and y is positive.</mcq-correct>
</answer>

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