Question

How did you determine the quadrant in which -1 radian will lie.

Answer 1

Hint:
 We will first understand what the is quadrant and the range of the angle which a particular quadrant represents and then we will determine the quadrant in which the -1 radian will lies.

Complete step by step answer:
We will first define the term quadrant. A coordinate plane can be divided into 4 regions or quadrants and each quadrant represents a particular range of angle measurement. An angle can be represented into the first, second, third, or fourth quadrant depending on which quadrant contains its terminal side.
The first quadrant represents the angle from 0 to $ \dfrac{\pi }{2} $ , means 0 to 1.57 radian. The second quadrant represents the angle from $ \dfrac{\pi }{2} $ to $ \pi $ , means 1.57 to 3.14 radian. The third quadrant represent the angle from $ \pi $ to $ \dfrac{3\pi }{2} $ , means 3.14 to 4.71 radian and the fourth quadrant represent angle from $ \dfrac{3\pi }{2} $ to $ 2\pi $ , means 4.17 to 6.28.
We will move in an anticlockwise direction to represent the positive angle and we will move in a clockwise direction to represent a negative angle. When move-in clockwise direction i.e. from x-axis towards -y-axis then angle decreases from 0 to $ -\dfrac{\pi }{2} $, means 0 to -1.57 radian and it is the fourth quadrant. Similarly, when we move from -y-axis to -x-axis then angle changes from $ -\dfrac{\pi }{2} $ to $ -\pi $, means -1.57 to -3.14 radian and it is in the third quadrant, Similarly, we can do for the others.
We can see from the question that -1 radian lies in between 0 and -1.57 radian and since we have seen above that we have to move in the clockwise direction to represent a negative angle, so -1 radian will lie in the fourth quadrant.
This is our required solution.

Note:
Students are required to note that when we have to find the quadrant of any angle which is greater than $ 2\pi $ lies, means angle greater than $ 360{}^\circ $ then we will first divide the given angle by $ 2\pi $ if it is in radian and by $ 360{}^\circ $ if it in degree, and obtain the remainder and then we will find the quadrant in which the remainder lies.