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Introduction to Trigonometry

Short Answer Type

131. Evaluate without using trigonometric tables:

fraction numerator 3 space cos space 55 degree over denominator 7 space sin space 35 degree end fraction minus fraction numerator 4 left parenthesis cos space 70 degree. space cosec space 20 degree right parenthesis over denominator 7 left parenthesis tan space 5 degree. space tan space 25 degree. space tan space 45 degree. space space tan space 65 degree. space tan space 85 degree right parenthesis end fraction.

147 Views

Long Answer Type

132.

Evaluate:
$space 2 over 3 cosec squared 58 degree space minus space 2 over 3 space cot space 58 degree space tan space 32 degree space minus space 5 over 3 space tan space 13 degree. space tan space 37 degree. space tan space 45 degree. space tan space 53 degree. space tan 77 degree.$

83 Views

Short Answer Type

133. Without using trigonometric tables, evalutate the following:

space space space left parenthesis sin squared 25 degree space plus space sin squared space 65 degree right parenthesis space plus space square root of 3 left parenthesis tan space 5 degree. space tan space 15 degree. space tan space 30 degree. space tan space 75 degree. space tan space 85 degree right parenthesis

130 Views

134. Without using the trigonometric tables, evaluate the following:

<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

110 Views

135. Evaluate without using trigonometric tables:

space space 2 open parentheses fraction numerator cos squared 20 degree plus cos squared 70 degree over denominator sin squared 25 degree plus sin squared 65 degree end fraction close parentheses minus tan space 45 degree plus space tan space 13 degree space tan space 23 degree space tan space 30 degree space tan space 67 degree space tan space 77 degree

103 Views

136. Without using the trigonometric tables, evaluate the following:

<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

75 Views

Long Answer Type

137. Without using trigonometric tables, evaluate.

<pre>uncaught exception: <b>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</b><br /><br />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<br />#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>

115 Views

138. Express the ratios cos A, tan A, cot A and sec A in terms of sin A.

198 Views

Short Answer Type

139. Prove the following identities:
$secA space left parenthesis 1 minus sinA right parenthesis thin space left parenthesis secA plus tanA right parenthesis space equals 1.$

sec A (1 - sin A) (sec A + tan A) = 1
L.H.S. = sec A (1 - sin A) (sec A + tan A)
$equals space 1 over cosA cross times left parenthesis 1 minus sinA right parenthesis space cross times space open parentheses 1 over cosA plus sinA over cosA close parentheses equals space open parentheses fraction numerator 1 minus sinA over denominator cosA end fraction close parentheses space open parentheses fraction numerator 1 plus sinA over denominator cosA end fraction close parentheses equals space fraction numerator left parenthesis 1 minus sinA right parenthesis thin space left parenthesis 1 plus sinA right parenthesis over denominator cos squared straight A end fraction space equals space fraction numerator 1 minus sin squared straight A over denominator cos squared straight A end fraction equals space fraction numerator cos squared straight A over denominator cos squared straight A end fraction space equals space 1 space equals space straight R. straight H. straight S.$
Hence, L.H.S. = R.H.S.

130 Views

Long Answer Type

140. Prove the following identities:

fraction numerator cot space straight A minus cos space straight A over denominator cot space straight A plus cos space straight A end fraction equals fraction numerator cosecA space minus 1 over denominator cosecA plus 1 end fraction.

90 Views