English

Find the angle in radian through which a pendulum swings if its length is 75 cm and the tip describes an arc of length 10 cm - Mathematics

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

10 cm

Sum
Advertisements

Solution

We know:

Radius = 75 cm

Length of the arc = 10 cm

Now,

\[\theta = \frac{\text{ Arc }}{\text{ Radius }}\]

\[ = \frac{10}{75}\]

\[ = \frac{2}{15} \text{ radian}\]

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Exercise 3.1 [Page 55]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise 3.1 | Q 7.1 | Page 55
RD Sharma Mathematics [English] Class 11
Chapter 4 Measurement of Angles
Exercise 4.1 | Q 14.1 | Page 15

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the radian measure corresponding to the following degree measure:

240°


Find the degree measure corresponding to the following radian measure (Use `pi = 22/7`)

-4


A wheel makes 360 revolutions in one minute. Through how many radians does it turn in one second?


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


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:
\[- \frac{5\pi}{6}\]


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: 
 11c


Find the degree measure corresponding to the following radian measure: 
 1c


Find the radian measure corresponding to the following degree measure:
300°


Find the radian measure corresponding to the following degree measure: 35°


Find the radian measure corresponding to the following degree measure: −56°


Find the radian measure corresponding to the following degree measure: −300°


Find the radian measure corresponding to the following degree measure: 125° 30'


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 pentagon.


Find the magnitude, in radians and degrees, of the interior angle of a regular heptagon.


Find the magnitude, in radians and degrees, of the interior angle of a regular duodecagon.


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

\[60^\circ, 80^\circ, 100^\circ\text{ and }120^\circ\], respectively.
Angles of the quadrilateral in radians =
\[\left( 60 \times \frac{\pi}{180} \right), \left( 80 \times \frac{\pi}{180} \right) , \left( 100 \times \frac{\pi}{180} \right) \text{ and }\left( 120 \times \frac{\pi}{180} \right)\]
\[\frac{\pi}{3}, \frac{4\pi}{9}, \frac{5\pi}{9}\text{ and } \frac{2\pi}{3}\]
 

 


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?

 

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 diameter of the sun in km supposing that it subtends an angle of 32' at the eye of an observer. Given that the distance of the sun is 91 × 106 km.

 

If the arcs of the same length in two circles subtend angles 65° and 110° at the centre, find the ratio of their radii.


Find the value of tan 9° – tan 27° – tan 63° + tan 81°


The value of tan1° tan2° tan3° ... tan89° is ______.


The value of cos1° cos2° cos3° ... cos179° is ______.


State whether the statement is True or False? Also give justification.

The equality sinA + sin2A + sin3A = 3 holds for some real value of A.


State whether the statement is True or False? Also give justification.

`cos  (2pi)/15 cos  (4pi)/15 cos  (8pi)/15 cos  (16pi)/15 = 1/16`


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×