Suppose theta is in the interval (90, 180). Choose whether the sign of tan(theta/2) is positive or negative.

Answers

Answer 1

Answer: $90^\circ<\theta<180^\circ\implies45^\circ<\frac\theta2<90^\circ$

$\tan\theta>0$ for $\theta$ in this interval.

Answer 2

Answer:

Final answer:

When theta is in the interval (90, 180), the sign of tan(theta/2) is negative.

Explanation:

When theta is in the interval (90, 180), the sign of tan(theta/2) is negative.

To understand why, we can use the half-angle identity for tangent:

tan(theta/2) = (-1 - cos(theta))/(sin(theta))
Since theta is in the second quadrant (90 < theta < 180), both sine and cosine are positive.
The numerator (-1 - cos(theta)) is negative, while the denominator (sin(theta)) is positive.
Therefore, the overall expression tan(theta/2) is negative.

Learn more about Tangent sign in second quadrant here:

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Answers

Answer:

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