Question
Write the value of $\cos^{-1}(\cos6).$

Answer

We know that $\cos^{-1}(\cos\text{x})=\text{x}$
Now,
$\cos^{-1}(\cos6)=\cos^{-1}\{\cos(2\pi-6)\}$
$=2\pi-6$

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

Similar questions

Compute $\left[\begin{array}{cc} {\cos ^{2} x} & {\sin ^{2} x} \\ {\sin ^{2} x} & {\cos ^{2} x} \end{array}\right]+\left[\begin{array}{cc} {\sin ^{2} x} & {\cos ^{2} x} \\ {\cos ^{2} x} & {\sin ^{2} x} \end{array}\right]$
If A = $\left[\begin{array}{ccc} {-1} & {2} & {3} \\ {5} & {7} & {9} \\ {-2} & {1} & {1} \end{array}\right]$ and B = $\left[\begin{array}{rrr} {-4} & {1} & {-5} \\ {1} & {2} & {0} \\ {1} & {3} & {1} \end{array}\right]$, then verify (A + B)′ = A′ + B′,
For what vaiue of $\lambda$ are the vectors $\vec{\text{a}}=2\hat{\text{i}}+\lambda\hat{\text{j}}+\hat{\text{k}}$ and $\vec{\text{b}}=\hat{\text{i}}-2\hat{\text{j}}+3\hat{\text{k}}$ perpendicular to each other?
Find the integral of the function $\frac{\cos x-\sin x}{1+\sin 2 x}$
Differentiate the $\sqrt{e^{\sqrt{x}}}, x>0$ w.r.t. x.
For what value of $\lambda$ is the function defined by
$\text{f(x)}= \begin{cases}\lambda(\text{x}^{2} - 2\text{x}), \text{if}\ \text{x} \leq0\\ \text{4x} + 1,\ \ \ \ \ \ \ \text{if}\ \text{x} > 0\end{cases}$
If $\text{A}=\begin{bmatrix}2 & 3 \\4 & 5 \end{bmatrix},$ prove that A - AT is a skew symmetric matrix.
Define vector product of two vectors.
Construct a 2 × 2 matrix A = [aij] whose elements aij are given by:
$\text{a}_\text{ij}=\frac{(\text{i}-\text{j})^2}{2}$
Find the value $k$, so that the given function is continuous at $x=5$
$
f(x)=\left\{\begin{array}{ccc}
k x+1 & \text { if } & x \leq 5 \\
3 x-5 & \text { if } & x>5
\end{array}\right.
$