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Chapter 4: Problem 26

Determine the quadrant in which each angle lies. (a) \(-132^{\circ} 50^{\prime}\) (b) \(-3.4^{\circ}\)

Short Answer

Expert verified
(a) The angle -132掳50' lies in the third quadrant. (b) The angle -3.4掳 lies in the fourth quadrant.

Step by step solution

01

Conversion of Minutes into Degrees

Firstly, one must convert minutes into degrees standardized system. A degree is divided into 60 minutes (hence, 1 minute = 1/60 degrees). So, for (a), the angle should be \(-132^{\circ} + \frac{-50^{\prime}}{60}\).
02

Conversion of Negative Angles

Next, handle the negative angles. Negative angle means the angle is measured in a clockwise direction instead of counter-clockwise. For angle in (a), its equivalent positive angle would be calculated by subtracting the obtained degree from 360 degrees. For (b), its positive equivalent will be found by subtracting -3.4 degrees from 360 degrees.
03

Determining the Quadrants

Knowing the measures of angles, find the quadrants. The first quadrant has angles from 0 to 90, the second 90 to 180, the third 180 to 270, and fourth from 270 to 360. Pinpoint which quadrant the angles from step 2 will fall into.

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