Advertisements
Advertisements
Question
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
Advertisements
Solution
We know:
Radius = 75 cm
Length of the arc = 15 cm
Now,
\[\theta = \frac{\text{Arc }}{\text{Radius}}\]
\[ = \frac{15}{75}\]
\[ = \frac{1}{5}\text{ radian }\]
RELATED QUESTIONS
Find the degree measure corresponding to the following radian measure (use `pi= 22/7`).
`(7pi)/6`
If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.
Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length
21 cm
Find the degree measure corresponding to the following radian measure:
\[\frac{9\pi}{5}\]
Find the degree measure corresponding to the following radian measure:
\[- \frac{5\pi}{6}\]
Find the degree measure corresponding to the following radian measure:
\[\left( \frac{18\pi}{5} \right)\]
Find the degree measure corresponding to the following radian measure:
(−3)c
Find the radian measure corresponding to the following degree measure:
300°
Find the radian measure corresponding to the following degree measure: 135°
The difference between the two acute angles of a right-angled triangle is \[\frac{2\pi}{5}\] radians. Express the angles in degrees.
One angle of a triangle \[\frac{2}{3}\] x grades and another is \[\frac{3}{2}\] x degrees while the third is \[\frac{\pi x}{75}\] radians. Express all the angles in degrees.
Find the magnitude, in radians and degrees, of the interior angle of a regular octagon.
Let the angles of the quadrilateral be \[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ \text{ and }\left( a + 3d \right)^\circ\]
We know: \[a - 3d + a - d + a + d + a - 2d = 360\]
\[ \Rightarrow 4a = 360\]
\[ \Rightarrow a = 90\]
We have:
Greatest angle = 120°
Now,
\[a + 3d = 120\]
\[ \Rightarrow 90 + 3d = 120\]
\[ \Rightarrow 3d = 30\]
\[ \Rightarrow d = 10\]
Hence,
\[\left( a - 3d \right)^\circ, \left( a - d \right)^\circ, \left( a + d \right)^\circ\text{ and }\left( a + 3d \right)^\circ\] are
Angles of the quadrilateral in radians =
The angles of a triangle are in A.P. and the number of degrees in the least angle is to the number of degrees in the mean angle as 1 : 120. Find the angles in radians.
The angles of a triangle are in A.P. such that the greatest is 5 times the least. Find the angles in radians.
The number of sides of two regular polygons are as 5 : 4 and the difference between their angles is 9°. Find the number of sides of the polygons.
A rail road curve is to be laid out on a circle. What radius should be used if the track is to change direction by 25° in a distance of 40 metres?
A wheel makes 360 revolutions per minute. Through how many radians does it turn in 1 second?
The radius of a circle is 30 cm. Find the length of an arc of this circle, if the length of the chord of the arc is 30 cm.
Find the distance from the eye at which a coin of 2 cm diameter should be held so as to conceal the full moon whose angular diameter is 31'.
Find the degree measure of the angle subtended at the centre of a circle of radius 100 cm by an arc of length 22 cm.
If the angles of a triangle are in A.P., then the measures of one of the angles in radians is
At 3:40, the hour and minute hands of a clock are inclined at
If OP makes 4 revolutions in one second, the angular velocity in radians per second is
The radius of the circle whose arc of length 15 π cm makes an angle of \[\frac{3\pi}{4}\] radian at the centre is
A circular wire of radius 3 cm is cut and bent so as to lie along the circumference of a hoop whose radius is 48 cm. Find the angle in degrees which is subtended at the centre of hoop.
If θ lies in the second quadrant, then show that `sqrt((1 - sin theta)/(1 + sin theta)) + sqrt((1 + sin theta)/(1 - sin theta))` = −2sec θ
Find the value of tan 9° – tan 27° – tan 63° + tan 81°
“The inequality `2^sintheta + 2^costheta ≥ 2^(1/sqrt(2))` holds for all real values of θ”
Which of the following is correct?
[Hint: 1 radian = `180^circ/pi = 57^circ30^'` approx]
