Question

Please help me!!
evaluate the expressions:
arctan(-√3)
Arctan(-√3)

Answer 1

Solution:-

To evaluate
`tan^(-1)(-√(3) )`

Consider a right angle triangle with base angle x =
`tan^(-1)(-√(3) )`

⇒tan x =
`(-√(3) )`

We know that for
`\theta`=60°, tan(60°)=
`√(3)`

here the value is
`(-√(3) )` so it will lie in 2nd or 4th quadrant.

For 2nd quadrant the value of x will be x=180°-
`\theta`

⇒ x=180°-60°=120°.

For 4th quadrant the value of x will be x=360°-
`\theta`

⇒ x=360°-60°=300°.

In radian

For 2nd quadrant the value of x will be x=180°-
`\theta`

⇒
`x=\pi-(\pi)/(3)=(2\pi)/(3)` =1.04(approx)

For 4th quadrant the value of x will be x=360°-
`\theta`

⇒
`x=2\pi-(\pi)/(3)=(5\pi)/(3)` .