Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; JCommentsACL has a deprecated constructor in /var/www/astarmathsandphysics/components/com_jcomments/classes/acl.php on line 17 Call Stack: 0.0001 360856 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0572 1211056 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0572 1211056 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1330 4044192 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1344 4071880 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1353 4089592 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1353 4106600 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1361 4114336 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1361 4114336 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1822 4354312 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1838 4371712 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1843 4392640 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.3082 9492552 13. JEventDispatcher->trigger() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:199 0.3084 9493000 14. plgContentJComments->update() /var/www/astarmathsandphysics/libraries/joomla/event/dispatcher.php:160 0.3084 9493000 15. plgContentJComments->onContentAfterDisplay() /var/www/astarmathsandphysics/libraries/joomla/event/event.php:70 0.3086 9501248 16. plgContentJComments->onAfterDisplayContent() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:339 0.3089 9502944 17. JComments::show() /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php:282 0.3095 9536224 18. JCommentsFactory::getACL() /var/www/astarmathsandphysics/components/com_jcomments/jcomments.php:188 0.3095 9536624 19. spl_autoload_call() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274 0.3096 9536704 20. JLoader::load() /var/www/astarmathsandphysics/components/com_jcomments/classes/factory.php:274

Equations With Reciprocal Trigonometric Functions

The reciprocal trigonometric functions areandGiven an equation of this sort we find the value oforfirst, then find the reciprocal of this to find the value oforthen solve this or these equation using the normal method for finding multiple angles of trigonometric formulae.

Example: Solve the formulafinding all solutions 0-360 degrees.

The expression factorises into

We follow the normal rule for quadratics by setting each factor equal to 0 and solving.

and

There are no other solutions in the range 0 – 360 degrees.

Example: Solve the formulafinding all solutions 0-360 degrees.

The expression factorises into

We follow the normal rule for quadratics by setting each factor equal to 0 and solving.

andand

and

Example: Solve the equationin the range 0 – 360 degrees.

or

or

oror

Add comment

Security code
Refresh