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Trigonometric Functions

Short Answer Type

541. Find 1 radian angle in degrees, minutes, seconds.

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542. Prove that the number of radians in an angle subtended by an arc of a circle at the centre = $space space fraction numerator arc space length over denominator radius end fraction$

Draw a circle of radius OA = r with centre at O.
Cut off an arc AB of length r and join OB; then $angle AOB space equals 1$ radian.
Cut off an another arc ABC of length l and join OC such that $angle AOC space equals space straight theta$ (radians). Since angles at the centre of the circle are proportional to the arcs on which they stand,

∴ $fraction numerator angle AOC over denominator angle AOB end fraction equals fraction numerator arc space ABC over denominator arc space AB end fraction space rightwards double arrow space space theta over 1 equals l over r space space space space rightwards double arrow space space space theta space left parenthesis r a d i a n s right parenthesis space equals space l over r$

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543.

Prove that:

$cos open parentheses straight pi over 2 minus straight x close parentheses space equals space sinx$

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544.

Prove that:

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

98 Views

Long Answer Type

545.

Prove the following:

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

111 Views

Short Answer Type

546.

Prove that:

$tan left parenthesis straight x plus straight y right parenthesis space equals space fraction numerator tanx plus tany over denominator 1 minus tanx space tany end fraction comma space space where space straight x comma straight y comma space straight x plus straight y space not equal to space left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 comma space straight n element of straight Z$

93 Views

547.

tan left parenthesis straight x minus straight y right parenthesis space equals space fraction numerator tanx minus tany over denominator 1 plus tanx space tany end fraction comma space where space straight x comma straight y comma space straight x minus straight y not equal to left parenthesis 2 straight n plus 1 right parenthesis straight pi over 2 comma space straight n element of straight Z

106 Views

548.

Prove that:

$tan open parentheses straight pi over 4 plus straight x close parentheses space equals space fraction numerator 1 plus tanx over denominator 1 minus tanx end fraction$

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549.

Prove that:

$space space space tan open parentheses straight pi over 4 minus straight x close parentheses space equals space fraction numerator 1 minus tanx over denominator 1 plus tanx end fraction$

109 Views

550.

Prove that:

$cos open parentheses straight pi over 2 plus straight x close parentheses space equals space minus sinx$

114 Views