Find the principal solutions of =-3 - Vidyadip

Question

Find the principal solutions of $\cot \theta=-\sqrt{3}$

✓

Answer

We know that $\cot \theta=-\sqrt{3}$ if and only if $\tan \theta=-\frac{1}{\sqrt{3}}$

We know that $\tan \frac{\pi}{6}=\frac{1}{\sqrt{3}}$

Using identities, $\tan (\pi-\theta)=-\tan \theta$ and $\tan (2 \pi-\theta)=-\tan \theta$, we get

$\tan \frac{5 \pi}{6}=-\frac{1}{\sqrt{3}}$ and $\tan \frac{11 \pi}{6}=-\frac{1}{\sqrt{3}}$

An $0 \leq \frac{5 \pi}{6}<2 \pi$ and $0 \leq \frac{11 \pi}{6}<2 \pi$

$\therefore \frac{5 \pi}{6}$ and $\frac{11 \pi}{6}$ are required principal solutions.

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 "Solve the Following Question.(2 Marks)" from Trigonometric Functions→Trigonometric Functions — all question types→Maths STD 12 Science question papers→Maharashtra Board STD 12 Science question papers→Maharashtra Board question paper generator→

Similar questions

If f(x) = x + 7 and g(x) = x - 7, x ∈ R, write fog (7).

Evaluate the following:
$\sec^{-1}\Big(\sec\frac{7\pi}{3}\Big)$

Evaluate the following integrals:$\int\limits^3_0\frac{1}{\text{x}^2+9}\text{ dx}$

Determine whether the following statement patterns are tautologies contradictions or contingencies : [p → (q → r)] ↔ [(p ∧ q) → r]

Find the value(s) of a for which $f(x)=x^3-a x$ is an increasing function on $R$.

If $\vec{\text{a}}$ is a unit vector, then find $|\vec{\text{x}}|$ in each of the following.$\big(\vec{\text{x}}-\vec{\text{a}}\big).\big(\vec{\text{x}}+\vec{\text{a}}\big)=8$

Find the principal solutions of $\cos \theta=-\frac{1}{2}$

Find the sum and the product of slopes of lines represented by $x^2+4 x y-7 y^2=0$.

A discrete random variable X has the probability distribution given below:

X:	0.5	1	1.5	2
P(X):	$k$	$k^2$	$2k^2$	$k$

Determine the mean of the distribution.

Differentiate the following w. r. t. x.$y=\cot ^2\left(x^3\right)$