Write the value of ^ -1 ( 5 4 ). - Vidyadip

Question

Write the value of $\cos^{-1}\Big(\cos\frac{5\pi}{4}\Big).$

✓

Answer

$\cos^{-1}\Big(\cos\frac{5\pi}{4}\Big)\neq\frac{5\pi}{4}$ as $\frac{5\pi}{4}$ does not lie between 0 and $\pi.$
We have
$\cos^{-1}\Big(\cos\frac{5\pi}{4}\Big)$
$=\cos^{-1}\Big\{\cos\Big(2\pi-\frac{3\pi}{4}\Big)\Big\}$
$=\cos^{-1}\Big\{\cos\Big(\frac{3\pi}{4}\Big)\Big\}$
$=\frac{3\pi}{4}$

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

Find the angle between the vectors $\vec{\text{a}} $ and $\vec{\text{b}},$ where

$\vec{\text{a}}=3\hat {\text{i}}-2\hat{\text{j}}-6\hat{\text{k}}$ and $\vec{\text{b}} =4\hat{\text{i}}-\hat{\text{j}}+8\hat{\text{k}}$

If $\vec{\text{a}},\ \vec{\text{b}},\ \vec{\text{c}}$ are non-coplanar vectors, prove that the given vectors are non-coplanar:
$2\vec{\text{a}}-\vec{\text{b}}+3\vec{\text{c}},\ \vec{\text{a}}+\vec{\text{b}}-2\vec{\text{c}}$ and $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$

Integrate the following integrals:
$\int\cos\text{mx}\cos\text{nx dx m}\neq\text{n}$

Evaluate the following integrals:
$\int\limits^\frac{\pi}{4}_0\tan\text{x dx}$

Show that the following systems of linear equations is inconsistent:

If $\vec{\text{a}}=3\hat{\text{i}}-\hat{\text{j}}+2\hat{\text{k}}$ and $\vec{\text{b}}=2\hat{\text{i}}+\hat{\text{j}}-\hat{\text{k}},$ then find $\big(\vec{\text{a}}\times\vec{\text{b}}\big)\vec{\text{a}}.$

If the matrix $\begin{bmatrix}5\text{x}&2\\-10&1\end{bmatrix}$ is a singular, find the value of x.

Discuss the continuity of the following functions at the indicated point:
$\text{f}\text{(x)}=\begin{cases}\text{(x}-\text{a})\sin\Big(\frac{1}{\text{x}-\text{a}}\Big), & \text{x} \neq 0\\\ \ 0, & \text{x} = \text{a}\end{cases}\text{at x}=\text{a}$

Write a unit vector in the direction of $\overrightarrow{\text{PQ}}$, where P and Q are the points (1, 3, 0) and (4, 5, 6) respectively.

The probability that a bulb produced by a factory will fuse after 150 days of use is 0.05. Find the probability that out of 5 such bulbs.
more than one.