Find an angle ,0< < 2 , which increases twice as fast as its sine… - Vidyadip

Question

Find an angle $\theta,0<\theta<\frac{\pi}{2},$ which increases twice as fast as its sine.

✓

Answer

Let $\theta$ increases twice as fast as its sine
$\Rightarrow\ \theta=2\sin\theta$
$\Rightarrow\ \frac{\text{d}\theta}{\text{dt}}=2\cdot\cos\theta\cdot\frac{\text{d}\theta}{\text{dt}}$
$\Rightarrow\ 1=2\cos\theta$
$\Rightarrow\ \frac{1}{2}=\cos\theta$
$\Rightarrow\ \cos\theta=\cos\frac{\pi}{3}$
$\therefore\ \theta=\frac{\pi}{3}$
So, the required angle is $\frac{\pi}{3}$

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 Questions" from APPLICATION OF DERIVATIVES→APPLICATION OF DERIVATIVES — all question types→Maths STD 12 Science question papers→Gujarat Board STD 12 Science question papers→Gujarat Board question paper generator→

Similar questions

If A is a square matrix of order $3$ such that $|A| = 5$, write the value of $|adj A|$.

Prove that for any two vectors $\vec{a}$ and $\vec{b}$, we always have $|\vec{a} \cdot \vec{b}| \leq|\vec{a}||\vec{b}|$ (CauchySchwartz inequality).

Find the particular solution of the differential equation $\frac{d y}{d x} = -4xy^2$ given that $y = 1$, when $x = 0$

Integrate the rational function $\frac{{2x}}{{\left( {{x^2} + 1} \right)\left( {{x^2} + 3} \right)}}$

If $A = \{1, 2, 3, 4\}$ and $B = \{a, b, c, d\}$ define any four bijections from $A$ to $B$. Also give their inverse functions.

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

If $\int\limits^{\text{a}}_03\text{x}^2\text{ dx}=8,$ Write the value of a.

Find the value of x, if:
if $\begin{vmatrix}3\text{x}&7\\2&4\end{vmatrix}=10,$ find the value of x.

Find the slope of the tangent to curve $y = x^3 – x + 1$ at the point whose x-coordinate is $2$.

If $\vec{\text{a}}$ and $\vec{\text{b}}$ are two vectors such that $\big|\vec{\text{a}}\big|=4,\big|\vec{\text{b}}\big|=3$ and $\vec{\text{a}}.\vec{\text{b}}=6,$ find the angle between $\vec{\text{a}}$ and $\vec{\text{b}}$.