English

Find the radian measure corresponding to the following degree measure: 240° - Mathematics

Advertisements
Advertisements

Question

Find the radian measure corresponding to the following degree measure:

240°

Sum
Advertisements

Solution

240°

We know that 180° = π radian

240° = `pi/180xx 240` radians = `(4pi)/3` radians

shaalaa.com
  Is there an error in this question or solution?
Chapter 3: Trigonometric Functions - Exercise 3.1 [Page 54]

APPEARS IN

NCERT Mathematics [English] Class 11
Chapter 3 Trigonometric Functions
Exercise 3.1 | Q 1.3 | Page 54

Video TutorialsVIEW ALL [1]

RELATED QUESTIONS

Find the radian measure corresponding to the following degree measure:

25°


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

`11/16`


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

-4


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

`(5pi)/3`


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


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

(Use `pi = 22/7`)


In a circle of diameter 40 cm, the length of a chord is 20 cm. Find the length of minor arc of the chord.


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

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


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.


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 =
\[\left( 60 \times \frac{\pi}{180} \right), \left( 80 \times \frac{\pi}{180} \right) , \left( 100 \times \frac{\pi}{180} \right) \text{ and }\left( 120 \times \frac{\pi}{180} \right)\]
\[\frac{\pi}{3}, \frac{4\pi}{9}, \frac{5\pi}{9}\text{ and } \frac{2\pi}{3}\]
 

 


The angle in one regular polygon is to that in another as 3 : 2 and the number of sides in first is twice that in the second. Determine the number of sides of two polygons.

 

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?

 

Find the length which at a distance of 5280 m will subtend an angle of 1' at the eye.

 

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.


If D, G and R denote respectively the number of degrees, grades and radians in an angle, the 


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


A circular wire of radius 7 cm is cut and bent again into an arc of a circle of radius 12 cm. The angle subtended by the arc 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.


Find the value of `sqrt(3)` cosec 20° – sec 20°


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°


If tan θ = `(-4)/3`, then sin θ is ______.


“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]


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

Sin10° is greater than cos10°


Share
Notifications

Englishहिंदीमराठी


      Forgot password?
Use app×