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Trigonometric Functions

Short Answer Type

11. Find the degree measure corresponding to the following radian measure:

11 over 16

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12. Find the degree measure corresponding to the following radian measure:

space space space space space fraction numerator 7 straight pi over denominator 6 end fraction

183 Views

13.

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

198 Views

14.

A wheel rotates through an angle of $straight pi over 30$ radians in one second. How many revolutions will it make in 5 minutes?

278 Views

15.

The difference between two acute angles of a right angled triangle is $fraction numerator 2 straight pi over denominator 5 end fraction radians.$ Express the angles in: (a) degrees (b) radians.

450 Views

16. If in two circles, arcs of the same length subtend angles 60° and 75° at the centre, find the ratio of their radii.

165 Views

17.

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 $straight pi space equals space 22 over 7$ ).

516 Views

18. A circular wire of radius 7.5 cm is cut and bent so as to lie along the circumference of a circular hoop whose radius is 120 cm. Find, in degrees, the angle which is subtended at the centre of this hoop.

1331 Views

19. A railway train is travelling on a circular track of 1500 m radius at the speed of 66 km/h. Through what angle (in degrees) does it turn in 10 seconds ?

155 Views

20.
An athlete runs 4 times around a circular running path to describe 1760 metres.

What is the angle in (i) radians, (ii) degrees subtended at the centre of the circle, when

he had run a distance of 308 metres? $open parentheses Take space straight pi space equals space 22 over 7 close parentheses$

Distance travelled in one round = $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$

Let r be the radius of the circular track.

∴ $<pre>uncaught exception: mkdir(): Permission denied (errno: 2) in /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php at line #56mkdir(): Permission denied in file: /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php line 56 #0 [internal function]: _hx_error_handler(2, 'mkdir(): Permis...', '/home/config_ad...', 56, Array) #1 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/util/sys/Store.class.php(56): mkdir('/home/config_ad...', 493) #2 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/FolderTreeStorageAndCache.class.php(110): com_wiris_util_sys_Store->mkdirs() #3 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/RenderImpl.class.php(231): com_wiris_plugin_impl_FolderTreeStorageAndCache->codeDigest('mml=<math xmlns...') #4 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/lib/com/wiris/plugin/impl/TextServiceImpl.class.php(59): com_wiris_plugin_impl_RenderImpl->computeDigest(NULL, Array) #5 /home/config_admin/public/felixventures.in/public/application/css/plugins/tiny_mce_wiris/integration/service.php(19): com_wiris_plugin_impl_TextServiceImpl->service('mathml2accessib...', Array) #6 {main}</pre>$ $rightwards double arrow$ $straight r space equals space fraction numerator 440 over denominator 2 straight pi end fraction space equals space fraction numerator 440 over denominator 2 cross times 22 end fraction cross times 7 space equals space 70 straight m$

Let the angle described in covering a distance of 308 metres be $straight theta$ radians.

Using $l over r space equals space straight theta comma$ we have

(i) $straight theta space equals space 308 over 70 radians space equals space 44 over 10 space equals space 4.4 space radians$

(ii) $straight theta space equals space 4.4 to the power of straight c space equals space open parentheses 44 over 10 cross times 180 over straight pi close parentheses to the power of degree space equals space open parentheses 44 over 10 cross times 180 cross times 7 over 22 close parentheses to the power of degree space equals space 252 to the power of ring operator$