Which quadrants show sine as a positive function?

Which quadrants show sine as a positive function?

• A. 1 and 3
• B. 2 and 3
• C. 1 and 4
• D. 2 and 4

Answer: (D)

To determine in which quadrants the sine function is positive, it's essential to understand the unit circle and the signs of the trigonometric functions in each quadrant. In the unit circle: - The first quadrant corresponds to angles from 0 to 90 degrees (or 0 to π/2 radians), where both sine and cosine are positive. Therefore, sine is positive in this quadrant. - The second quadrant covers angles from 90 degrees to 180 degrees (or π/2 to π radians). In this quadrant, sine remains positive while cosine is negative. Thus, sine is also positive in the second quadrant. - The third quadrant spans angles from 180 degrees to 270 degrees (or π to 3π/2 radians), where both sine and cosine are negative. In this quadrant, sine is not positive. - The fourth quadrant includes angles from 270 degrees to 360 degrees (or 3π/2 to 2π radians), where sine is again negative while cosine is positive. This means sine is also not positive here. Since sine is positive in the first and second quadrants, the correct identification of those quadrants is the first and second, not the second and fourth. Hence, the statement that the correct

To determine in which quadrants the sine function is positive, it's essential to understand the unit circle and the signs of the trigonometric functions in each quadrant.

In the unit circle:

• The first quadrant corresponds to angles from 0 to 90 degrees (or 0 to π/2 radians), where both sine and cosine are positive. Therefore, sine is positive in this quadrant.

• The second quadrant covers angles from 90 degrees to 180 degrees (or π/2 to π radians). In this quadrant, sine remains positive while cosine is negative. Thus, sine is also positive in the second quadrant.

• The third quadrant spans angles from 180 degrees to 270 degrees (or π to 3π/2 radians), where both sine and cosine are negative. In this quadrant, sine is not positive.

• The fourth quadrant includes angles from 270 degrees to 360 degrees (or 3π/2 to 2π radians), where sine is again negative while cosine is positive. This means sine is also not positive here.

Since sine is positive in the first and second quadrants, the correct identification of those quadrants is the first and second, not the second and fourth. Hence, the statement that the correct