Question

Principal value of $\tan\theta = - 1$ is

• A. $\frac{- \pi}{4}$
• B. $\frac{\pi}{4}$
• C. $\frac{3\pi}{4}$
• D. $\frac{- 3\pi}{4}$

Answer 1

Answer: (A)

$\frac{- \pi}{4}$

Answer 2

$\bullet \bullet$ $\tan\theta$is negative.

$\therefore$ $\theta$ will lie in 2^nd or 4^th quadrant. For 2^nd quadrant we will

select anticlockwise and for 4^th quadrant, we will select

clockwise direction.

In the first circle two values $\frac{- \pi}{4}$ and $\frac{3\pi}{4}$are obtained.

Among these two, $\frac{- \pi}{4}$ is numerically least angle. Hence

principal value is $\frac{- \pi}{4}.$