Questions: Suppose θ is in the interval 90°<θ<180°. Find the sign of the following. sin(θ+90°) Choose whether the sign of sin (θ+90°) is positive or negative. Negative Positive

Suppose θ is in the interval 90°<θ<180°. Find the sign of the following. sin(θ+90°) Choose whether the sign of sin (θ+90°) is positive or negative. Negative Positive
Transcript text: Suppose $\theta$ is in the interval $90^{\circ}<\theta<180^{\circ}$. Find the sign of the following. \[ \boldsymbol{\operatorname { s i n }}\left(\theta+90^{\circ}\right) \] Choose whether the $\operatorname{sign}$ of $\sin \left(\theta+90^{\circ}\right)$ is positive or negative. Negative Positive
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Solution

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Solution Steps

Step 1: Identify the Quadrant

The original angle \(\theta = 135^\circ\) lies in the second quadrant. After applying the transformation +90, the angle becomes \(\theta = 225^\circ\). This places the angle in the 3 quadrant.

Step 2: Apply Trigonometric Function Signs

In the 3 quadrant, the sign of the sin function is '-'.

Final Answer:

The sign of the sin function, after applying the transformation +90 to an angle in the second quadrant, is '-'.

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