Problem 121
Question
If \(\theta=\frac{3}{2},\) is this angle larger or smaller than a right angle?
Step-by-Step Solution
Verified Answer
The given angle \(\theta=\frac{3}{2}\) is larger than a right angle.
1Step 1: Conversion of Right Angle into Radians
Firstly, convert the right angle into radians, so it can be compared to the given angle. A right angle is defined as 90 degrees. In terms of radians, it is \( \frac{\pi}{2}\) radians.
2Step 2: Comparison of Angles
Next, compare the given angle \(\theta=\frac{3}{2}\) with the right angle \( \frac{\pi}{2}\). Since \( \pi \) is approximately 3.14, the right angle in radians would be approximately 1.57. So, \( \frac{3}{2}\) is larger than the value of a right angle in radians.
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