When solving trigonometric equations, in which quadrants is sine positive?

Sine is positive in the first and second quadrants of the unit circle. To understand this, it's important to consider the definitions of the sine function and how the unit circle is structured.

In the first quadrant, both the x-coordinates (cosine values) and y-coordinates (sine values) of points on the unit circle are positive. Therefore, since sine corresponds to the y-coordinate, it will also be positive in this quadrant.

In the second quadrant, the x-coordinates are negative while the y-coordinates remain positive. Thus, even though cosine (the x-value) is negative, the sine (the y-value) is still positive in this quadrant.

In contrast, sine becomes negative in the third quadrant where both the x and y coordinates are negative, and also in the fourth quadrant where the x-coordinates are positive but y-coordinates are negative. Therefore, it is only in the first and second quadrants that sine maintains positive values. This understanding provides a clear reason why the first and second quadrants are the correct answer regarding the positivity of the sine function.