Mathematics: In what quadrant does the angle 2x/3 terminate?

In what quadrant does the angle 2x/3 terminate?

Ответ:

gloriuos355

14.03.2022

Mathematics

Second quadrant.

Step-by-step explanation:

The given angle is

$\frac{2 \pi}{3}$

To know where this angle terminates, first, we need to transform it into degrees.

We know that $\pi = 180 \°$

So,

$\frac{2 \pi}{3}=\frac{2 (180\°)}{3}=2(60\°)=120\°$

Now, each quadrant is delimited by an angle interval:

I quadrant from 0° to 90°.II quadrant from 90° to 180°.III quadrant from 180° to 270°.IV quadrant from 270° to 360°.

Our angle is 120°, that means it terminates inside the second quadrant, because it's determined by the range 90° - 180°, and 120° is inside.

Therefore, the given angle terminates in the second quadrant.

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Ответ:

emilybutler

30.12.2020

Mathematics

$x+y =6 ~~~.....(i)\\\\x =3y -2~~.....(ii)\\\\\text{Substitute}~ x =3y-2~ \text{in equation (i):}\\\\\\3y -2 +y =6\\\\\implies 4y = 6+2\\\\\implies 4y = 8\\\\\\\implies y =\dfrac 84 =2\\\\\text{Substitute y =2 in equation (ii):}\\\\x = 3(2) -2\\\\\implies x = 6-2 =4\\\\\\\text{Hence,}~ (x,y) = \left(4, 2\right)$

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In what quadrant does the angle 2x/3 terminate?

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