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

Solution

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 '-'.