Final Answer:
The sign of sec(θ + 180°) in the interval (90°, 180°) is -1.
Step-by-step explanation:
In the given interval (90°, 180°), θ lies in the second quadrant. The secant function is the reciprocal of the cosine function, and in the second quadrant, cosine is negative. When we add 180° to θ, we move to the third quadrant where both sine and cosine are negative.
In the third quadrant, the cosine is negative, and since secant is the reciprocal of cosine, secant is negative as well. Therefore, sec(θ + 180°) will have a negative sign in this interval. This is because the cosine of (θ + 180°) is negative, and when we take the reciprocal, the sign becomes negative. In mathematical terms, if cos(θ) is negative, then sec(θ) will be negative.
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