Trigonometry

**hoanghai549** · February 22nd 2011, 02:02 AM

If y= arctan x and x<0 then y lies in what quadrant ?

**sa-ri-ga-ma** · February 22nd 2011, 02:14 AM

In the co-ordinate axis, if the angle subtended at the origin is θ, then tanθ = y/x. tanθ will be negative when x will be negative of y will be negative. Now decide in which quadrant the angle will be?

**emakarov** · February 22nd 2011, 02:31 AM

tanθ will be negative when x will be negative of y will be negative.

$\tan\theta<0$ when x < 0 and y > 0 or y < 0 and x > 0. Also, one must take into account that arctan returns angles between $-\pi/2$ and $\pi/2$ .

**Soroban** · February 22nd 2011, 05:14 AM

Hello, hoanghai549!

$\text{If }y\,=\, \arctan x\,\text{ and }\,x<0,\,\text{ then }y\text{ lies in what quadrant?}$

We have: . $y\,=\,\arctan x \quad\Rightarrow\quad \tan y \,=\,x\;\;\text{ and }x\text{ is negative.}$

The tangent function is negative in Quadrants 2 and 4.

**hoanghai549** · February 22nd 2011, 06:49 AM

Originally Posted by Soroban

Hello, hoanghai549!

We have: . $y\,=\,\arctan x \quad\Rightarrow\quad \tan y \,=\,x\;\;\text{ and }x\text{ is negative.}$

The tangent function is negative in Quadrants 2 and 4.

Could you elaborate it in detail ? I have confused on it .

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