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The terminal side of an angle θ in standard position intersects the unit circle at 12 37 , – 35 37 . What is sin(θ)?

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3 votes

Answer:

The correct answer is 35/37

Step-by-step explanation: it wouldn't be a negative

User Wannik
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2 votes

Final answer:

The value of sin(θ) where θ intersects the unit circle at (12/37, -35/37) is -35/37, since the y-coordinate represents the sine value on the unit circle.

Step-by-step explanation:

To find the value of sin(θ) when the terminal side of an angle θ in standard position intersects the unit circle at the point (12/37, –35/37), we recall that on the unit circle, the y-coordinate of the point gives the value of the sine of the angle. Therefore, the value of sin(θ) is the y-coordinate of the point where the terminal side intersects the unit circle.

In this case, the y-coordinate is -35/37. Hence, sin(θ) = -35/37.

Remember that the range of the sine function is from -1 to 1 and that it represents the ratio of the length of the side opposite to the angle to the hypotenuse in a right-angle triangle. This concept is depicted in trigonometry and unit circle frameworks, as the sine function correlates with the vertical coordinate of a unit circle.

User Nirav Zaveri
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