Find the principal values: ^ -1 (-1 2 ) - Vidyadip

Question

Find the principal values:
$\cos^{-1}\left(-\frac{1}{2}\right)$

✓

Answer

$\text{Let}=\cos^{-1}\bigg(-\frac{1}{2}\bigg)=\text{Y where}\ 0\leq\text{Y}\leq{\pi}$
$ \therefore\ \ \ \ \cos\text{Y}=-\frac{1}{2} \text{where}\ 0\leq\text{Y} \leq {\pi}$
$\Rightarrow\ \ \ \text{Y}=\frac{2\pi}{3}$, $\left[\because\ \cos\frac{2\pi}{3}=\cos\left({\pi}-\frac{{\pi}}{3}\right)=-\cos\frac{{\pi}}{3}=-\frac{1}{2}\right]$
$\therefore$ required principal value $=\frac{2\pi}{3}$

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 "2 Marks" from INVERSE TRIGNOMETRIC FUNCTIONS→INVERSE TRIGNOMETRIC FUNCTIONS — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

Matrix $\text{A}=\begin{bmatrix}0&2\text{b}&-2\\3&1&3\\3\text{a}&3&-1 \end{bmatrix}$ is given to be symmetric, find values of a and b.

Show that
$\sin ^{-1}(2 x \sqrt{1-x^{2}})=2 \sin ^{-1} x,-\frac{1}{\sqrt{2}} \leq x \leq \frac{1}{\sqrt{2}}$

Evaluate the following determinant:
$\begin{vmatrix}\text{a}&\text{h}&\text{g}\\\text{h}&\text{b}&\text{f}\\\text{g}&\text{f}&\text{c}\end{vmatrix}$

Find the position vector of the min-point of the line segment AB, where A is the point (3, 4, -2) and B is the point (1, 2, 4).

Find a unit vector perpendicular to vectors $(\vec{a}+\vec{b})$ and $(\vec{a}-\vec{b})$, when $\vec{a}=2 \hat{i}+\hat{j}-2 \hat{k}, \vec{b}=\hat{i}-2 \hat{j}+2 \hat{k}$

If A and B are non-singular matrices of the same order, write whether AB is singular or non-singular.

A bag contains 6 black and 3 white balls. Another bag contains 5 black and 4 white balls. If one ball is drawn from each bag, find the probability that these two balls are of the same colour.

Evaluate the following determinant:
$\begin{vmatrix}67&19&21\\39&13&14\\81&24&26 \end{vmatrix}$

If $\begin{vmatrix}3\text{x}&7\\-2&4\end{vmatrix}=\begin{vmatrix}8&7\\6&4\end{vmatrix},$ find the value of x.

For each binary operation * defined below, determine whether * is commutative or associative.
On Q, define $\text{a} * \text{b} =\frac{\text{ab}}{2}$