Explaining the relationship between sine of an angle in the second quadrant and its negative counterpart, suitable for high school students.
When an angle θ is in the second quadrant, the sine of that angle is positive. Therefore, if we know that sin(θ) = 0.809, this means that the sine value is positive.
However, for the angle –θ (the angle reflected over the x-axis), it will be in the fourth quadrant, where sine values are negative. Thus, we can conclude:
sin(-θ) = -sin(θ) = -0.809.
This indicates that sin(-θ) will be negative, specifically sin(-θ) = -0.809.
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