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Trigonometric Functions

Short Answer Type

131. Find the principal and general solutions of the following equations:

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127 Views

132. Find the principal and general solutions of the following equation:

$sec space straight x space equals space 2$

$sec space straight x space equals space 2$

$rightwards double arrow$ $cosx space equals space 1 half$ is positive.

∴ x lies in quadrant I or quadrant IV.

∴ $space space space cos space straight x space equals space 1 half space equals space cos space 60 degree$ or $cos space left parenthesis 360 degree space minus space 60 degree right parenthesis space equals space cos space 60 degree space space or space space cos space 300 degree$

 $equals space cos open parentheses straight pi over 3 close parentheses space or space cos open parentheses fraction numerator 5 straight pi over denominator 3 end fraction close parentheses$

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

Now, $space space space cos space straight x space equals space 1 half space equals space cos open parentheses straight pi over 3 close parentheses space rightwards double arrow space straight x space equals space 2 nπ plus-or-minus straight pi over 3 comma space space straight n element of straight Z$

120 Views

133. Find the principal and general solutions of the following equation:

cot space straight x space equals space minus square root of 3

138 Views

134. Find the principal and general solutions of the following equation:

cosec space straight x space equals space minus 2

115 Views

135. Find the general solution of the following equation:

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111 Views

136. Find the general solution of the following equation:

sin space 2 straight x space equals space cos space straight x space

136 Views

137. Find the general solution of the following equation:

sin x + sin 3x + sin 5x = 0

145 Views

138. Find the general solution of the following equation:

cos 3x + cos x - cos 2x = 0

164 Views

139.

Find the general solution of:

$2 space cos squared straight x space minus space 5 space cosx space plus space 2 space equals space 0$

121 Views

140.

Find the general solution of:

$space space space 4 space sin squared straight theta space minus space 8 space cosθ space plus space 1 space equals 0$

138 Views