Question

in which quadant sin 3pie/2+ x lies

Answer 1

Explanation:

Cartesian plane is divided into four quadrants.
In first quadrant we have both abscissa and ordinates positive. In this quadrant, if we join the point to origin, the angle formed by this line with positive side of x-axis, say θ is between 0∘ and 90∘ or π2 (in radians), which we can write as 0<θ<π2.
In second quadrant while abscissa is negative, ordinate is positive. In this quadrant, if we join the point to origin, the angle θ formed by this line with positive side of x-axis is between 90∘ and 180∘ or between π2 and π, which we can write as π2<θ<π.
In third quadrant while abscissa and ordinate both are negative. In this quadrant, if we join the point to origin, the angle θ formed by this line with positive side of x-axis is between 180∘ and 270∘ or between π and 3π2, which we can write as π<θ<3π2.
In fourth quadrant while abscissa is positive, ordinate is negative. In this quadrant, if we join the point to origin, the angle θ formed by this line with positive side of x-axis is between 270∘ and 360∘ or between 3π2 and 2π, which we can write as 3π2<θ<2π.
https://www.mathsisfun.com/algebra/trig-four-quadrants.html
Hence while π<a<3π2 refers to Q3, 3π2<B<2π refers to Q4

Answer 2

Its in quad 4, its in quad 4