Find the angle in radian through which a pendulum swings if its length is $75\, cm$ and the tip describes an arc of length.
$15\,cm$
We know that in a circle of radius $r$ unit, if an arc of length $l$ unit subtends
An angle $\theta$ radian at the centre, then $\theta=\frac{l}{r}$
It is given that $r=75\, cm$
Here, $l=15\, cm$
$\theta=\frac{15}{75}$ radian
$=\frac{1}{5}$ radian
If the arcs of the same lengths in two circles subtend angles $65^{\circ}$ and $110^{\circ}$ at the centre, find the ratio of their radii.
If $\cos (\alpha - \beta ) = 1$ and $\cos (\alpha + \beta ) = \frac{1}{e}$, $ - \pi < \alpha ,\beta < \pi $, then total number of ordered pair of $(\alpha ,\beta )$ is
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If $x = \sec \,\phi - \tan \phi ,y = {\rm{cosec}}\phi + \cot \phi ,$ then
In a right angled triangle the hypotenuse is $2 \sqrt 2$ times the perpendicular drawn from the opposite vertex. Then the other acute angles of the triangle are