Evaluate the following: ^ -1 (4 3 ) - Vidyadip

Question

Evaluate the following:
$\cos^{-1}\Big\{\cos\Big(\frac{4\pi}{3}\Big)\Big\}$

✓

Answer

We know that,
$\cos^{-1}\big(\cos\theta\big)=\begin{cases}-\theta,&\text{if }\theta\in[-\pi,0]\\\theta,&\text{if }\theta\in[0,\pi]\\2\pi-\theta,&\text{if }\theta\in[\pi,2\pi]\\-2\pi+\theta,&\text{if }\theta\in[2\pi,3\pi]\end{cases}$
We have
$\cos^{-1}\Big\{\cos\Big(\frac{4\pi}{3}\Big)\Big\}=\cos^{-1}\Big\{\cos\Big(2\pi-\frac{2\pi}{3}\Big)\Big\}$
$\cos^{-1}\Big\{\cos\Big(\frac{2\pi}{3}\Big)\Big\}$
$=\frac{2\pi}{4}$

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 "Solve the Following Question.(2 Marks)" from Inverse Trigonometric Functions→Inverse 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

A fair coin is tossed 8 times, find the probability of.
at least six heads.

Find the vector equation of the line which passes through the origin and the point (5, -2, 3).

Evaluate $\int\frac{\text{x}^3-\text{x}^2+\text{x}+1}{\text{x}-1}\text{ dx}$

Find the general solutions of the following equations :

sin θ – cosθ = 1

Determine the order and degree of each of the following differential equations:

$\frac{d^2 y}{d t^2}+\left(\frac{d y}{d t}\right)^2+7 x+5=0$

If two non-zero vectors $\bar{a}$ and $\bar{b}$ are collinear then prove that there exist scalars $m$ and $n$ such that $m \bar{a}+n \bar{b}=\overline{0}$ and $(m, n) \neq(0,0)$.

If $\text{y}=1-\text{x}+\frac{\text{x}^2}{2!}-\frac{\text{x}^3}{3!}+\frac{\text{x}^4}{4!}+...\infty$ then write $\frac{\text{d}^2\text{y}}{\text{dx}^2}$ in terms of y.

Diffrentiate the following w.r.t.x

$\cos \left(x^2+a^2\right)$

Find the direction ratios of a vector perpendicular to the two lines whose direction ratios are $1, 3, 2$ and $–1, 1, 2$

Evaluate the following integrals:$\int\limits^2_0\big[\text{x}\big]\text{dx}$