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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

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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:

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

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

As we know that:

$tan space left parenthesis straight x plus straight y right parenthesis space equals space fraction numerator tanx plus tany over denominator 1 minus tanx space tany end fraction$

Replacing y by -y, we get

$tan left parenthesis straight x minus straight y right parenthesis space equals space fraction numerator tanx plus tan left parenthesis negative straight y right parenthesis over denominator 1 minus tanx space tan left parenthesis negative straight y right parenthesis end fraction space equals space fraction numerator tanx minus tany over denominator 1 plus tanx space tany end fraction$ [∵ tan (-y) = -tany]

Hence, $tan left parenthesis straight x minus straight y right parenthesis equals fraction numerator tanx minus tany over denominator 1 plus tanx space tany end fraction$

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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:

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

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550.

Prove that:

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

114 Views