Deprecated: Methods with the same name as their class will not be constructors in a future version of PHP; plgContentJComments has a deprecated constructor in /var/www/astarmathsandphysics/plugins/content/jcomments/jcomments.php on line 25 Call Stack: 0.0001 362584 1. {main}() /var/www/astarmathsandphysics/index.php:0 0.0520 1212024 2. Joomla\CMS\Application\SiteApplication->execute() /var/www/astarmathsandphysics/index.php:49 0.0520 1212024 3. Joomla\CMS\Application\SiteApplication->doExecute() /var/www/astarmathsandphysics/libraries/src/Application/CMSApplication.php:267 0.1199 4193144 4. Joomla\CMS\Application\SiteApplication->dispatch() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:233 0.1212 4220824 5. Joomla\CMS\Component\ComponentHelper::renderComponent() /var/www/astarmathsandphysics/libraries/src/Application/SiteApplication.php:194 0.1218 4238536 6. Joomla\CMS\Component\ComponentHelper::executeComponent() /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:356 0.1220 4269056 7. require_once('/var/www/astarmathsandphysics/components/com_content/content.php') /var/www/astarmathsandphysics/libraries/src/Component/ComponentHelper.php:381 0.1231 4291776 8. ContentController->execute() /var/www/astarmathsandphysics/components/com_content/content.php:42 0.1231 4291776 9. ContentController->display() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:710 0.1772 4973632 10. ContentController->display() /var/www/astarmathsandphysics/components/com_content/controller.php:113 0.1806 5165784 11. Joomla\CMS\Cache\Controller\ViewController->get() /var/www/astarmathsandphysics/libraries/src/MVC/Controller/BaseController.php:663 0.1811 5186712 12. ContentViewArticle->display() /var/www/astarmathsandphysics/libraries/src/Cache/Controller/ViewController.php:102 0.1923 5387896 13. Joomla\CMS\Plugin\PluginHelper::importPlugin() /var/www/astarmathsandphysics/components/com_content/views/article/view.html.php:189 0.1923 5388152 14. Joomla\CMS\Plugin\PluginHelper::import() /var/www/astarmathsandphysics/libraries/src/Plugin/PluginHelper.php:182

Using the Angle Sum Formulae to Solve Trigonometric Equations

To solve an equation of the form

1. Expand both sides using the angle sum formulae:

(1)

(2)

(3)

(4)

2. Divide through byto obtain terms in

3. Transfer the terms into one side.will now be a common factor. Factorise with

3. Makethe subject andboth sides.

Example: Solve

The problem becomes

Divide byto obtain

Rearrange to give

Factorise with

Make tan x the subject:and arctan to give