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 Questions" from Inverse Trigonometric Functions→Inverse Trigonometric Functions — all question types→MATHS STD 12 Science question papers→Rajasthan Board STD 12 Science question papers→Rajasthan Board question paper generator→

Similar questions

Evalute the following integrals:
$\int\frac{1-\sin2\text{x}}{\text{x}+\cos^2\text{x}}\text{dx}$

Construct a 3 × 2 matrix whose elements are given by $\text{a}_{\text{ij}}=\text{e}^{\text{i.x}}=\sin\text{jx}.$

Evaluate the following integrals:
$\int\big(\text{x}^\text{e}+\text{e}^\text{x}+\text{e}^\text{e}\big)\text{dx}$

Write the identity element for the binary operation * defined on the set R of all real numbers by the rule $\text{a}\times\text{b}=\frac{3\text{ab}}{7}\ \forall\text{ a, b}\in\text{R}$.

Show that the relation R in the set {1, 2, 3} given by R = {(1, 2), (2, 1)} is symmetric but neither reflexive nor transitive.

Show that the function $f$ given by $f(x)=\left\{\begin{array}{ll} {x^{3}+3,} & {\text { if } x \neq 0} \\ {1,} & {\text { if } x=0} \end{array}\right.$ is not continuous at $x = 0$.

Examine the following functions for continuity.
$f(x) = \frac{1}{\text{x}-5}$

Evaluate the following integrals:
$\int\Big(\sqrt{\text{x}}-\frac{1}{\sqrt{\text{x}}}\Big)^2\text{dx}$

Verify that the function $y=x \sin 3 x$ (implicit or explicit) is a solution of the differential equation $\frac{d^{2} y}{d x^{2}}+9 y-6 \cos 3 x=0$

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 $\vec{\text{a}}+\vec{\text{b}}-3\vec{\text{c}}$