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Question

of ordered pairs which satisfy the equation $x to the power of 2 end exponent plus 2 x sin invisible function application open parentheses x y close parentheses plus 1 equals 0$ are $blank$ (where $y element of open square brackets 0 comma blank 2 pi close square brackets right parenthesis$

1
2
3
0

The correct answer is: 2

Given $x to the power of 2 end exponent plus 2 x sin invisible function application open parentheses x comma y close parentheses plus 1 equals 0$
$rightwards arrow open square brackets x plus sin invisible function application open parentheses x y close parentheses close square brackets to the power of 2 end exponent plus open square brackets 1 minus sin to the power of 2 end exponent invisible function application open parentheses x y close parentheses close square brackets equals 0$
$rightwards arrow x plus sin invisible function application open parentheses x y close parentheses equals 0$ and $sin to the power of 2 end exponent invisible function application open parentheses x y close parentheses equals 1$
$sin to the power of 2 end exponent invisible function application open parentheses x y close parentheses equals 1 blank$ gives $sin invisible function application open parentheses x y close parentheses equals 1$ or $negative 1$
If $sin invisible function application open parentheses x y close parentheses equals 1 rightwards double arrow x equals negative 1 blank rightwards double arrow sin invisible function application open parentheses negative y close parentheses equals 1 rightwards double arrow sin invisible function application y equals negative 1 comma$ then $blank$
The ordered pair is $left parenthesis 1 comma blank 3 pi divided by 2 right parenthesis$
If $sin invisible function application open parentheses x y close parentheses equals negative 1 blank rightwards double arrow x equals 1 blank rightwards double arrow sin invisible function application y equals negative 1 blank rightwards double arrow open parentheses negative 1 comma blank 3 pi divided by 2 close parentheses$
Thus, there are two ordered pairs

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