Find the principal values of: ^ -1 (-3) - Vidyadip

MCQ

Find the principal values of: $\cot ^{-1}(-\sqrt{3})$

✓
$\frac{5 \pi}{6}$
B
$\frac{\pi}{3}$
C
$\frac{\pi}{2}$
D
$\frac{\pi}{4}$

✓

Answer

Correct option: A.

$\frac{5 \pi}{6}$

(a) : Let $\cot ^{-1}(-\sqrt{3})=\theta \Rightarrow \cot \theta=-\sqrt{3}=-\cot \frac{\pi}{6}$
$=\cot \left(\pi-\frac{\pi}{6}\right)=\cot \frac{5 \pi}{6} \Rightarrow \theta=\frac{5 \pi}{6} \in(0, \pi)$
$\therefore$ Principal value of $\cot ^{-1}(-\sqrt{3})$ is $\frac{5 \pi}{6}$.

Need a full question paper?

Generate a complete, print-ready paper with questions like this in minutes — across 16+ boards, with answer keys.

Start Generating Free

Explore more

More "M.C.Q (1 Marks)" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If $\text{f}(\text{x})=\sqrt{\text{x}^2+6\text{x}+9},$ then f'(x) is equal to:

1 for x < -3
-1 for x < -3
1 for all $\text{x}\in\text{R}$
None of these.

A constraint in an LP model becomes redundant because:

${\sin ^{ - 1}}\left( {\frac{3}{5}} \right) + {\tan ^{ - 1}}\left( {\frac{1}{7}} \right) = $

Let $f(x)=\min \{[x-1],[x-2], \ldots,[x-10]\}$ where $[ t$ ] denotes the greatest integer $\leq t$.Then$\int_{0}^{10} f(x) d x+\int_{0}^{10}(f(x))^{2} d x+\int_{0}^{10}|f(x)| d x$ is equal to

One ticket is selected at random from $50$ tickets numbered $00,01,02, ... ,49.$ Then the probability that the sum ofthe digits on the selected ticket is $8$, given that the product of these digits is zero, equals:

Choose the correct answer from the given four options:
The area of the region bounded by the curve x = 2y + 3 and the y lines. y = 1 and y = -1 is:

$4\text{ sq. units}$
$\frac{3}{2}\text{ sq. units}$
$6\text{ sq. units}$
$8\text{ sq. units}$

Find the area of bounded by $\text{y}=\sin\text{x}$ from $\text{x}=\frac{\pi}{4}$ to $\text{x}=\frac{\pi}{2}:$

$\frac{\sqrt{2-1}}{\sqrt2}$
$\frac{1}{2}$
$\frac{1}{4}$
$\text{none}\text{ of}\text{ these}$

For any two vectors $\vec{a}$ and $\vec{b}$, which of the following statements is always true?

The circumference of a circle is measured as 28cm with an error of 0.01cm. The percentage error in the area is:

$\frac{1}{14}$
$0.01$
$\frac{1}{7}$
$\text{None of these}$

Let $a, b$ and $c$ be distinct positive numbers. If the vectors $a \hat{i}+a \hat{j}+c \hat{k}, \hat{i}+\hat{k}$ and $c \hat{i}+c \hat{j}+b \hat{k}$ are co-planar, then $\mathrm{c}$ is equal to: