How to open a modal in javascript instead of manual click? [duplicate]

I have a modal which is open when i click on a button. Now i want to open the modal in a javascript function. Here is the working modal :

<a href="#" class="btn btn-lg btn-primary" id="sentMessage" data-toggle="modal" data-target="#largeModal">Click to open Modal</a>
    <div class="modal fade" id="largeModal" tabindex="-1" role="dialog" aria-labelledby="largeModal" aria-hidden="true">
      <div class="modal-dialog modal-lg">
        <div class="modal-content">
          <div class="modal-header">
            <button type="button" class="close" data-dismiss="modal" aria-hidden="true">&times;</button>
            <h4 class="modal-title" id="myModalLabel">Large Modal</h4>
          </div>
          <div class="modal-body">
            <h3>Modal Body</h3>
          </div>
          <div class="modal-footer">
            <button type="button" class="btn btn-default" data-dismiss="modal">Close</button>
            <button type="button" class="btn btn-primary">Save changes</button>
          </div>
        </div>
      </div>
    </div>

I want to open the same modal in a javascript function. So to simulate this function, i create another button which trigger a function :

<a href="#" ng-click="openModal();" class="btn btn-lg btn-primary">Click to execute js</a>

Here is my openModal function :

$scope.openModal = function(){
    $("#sentMessage").click();

};

When i click on the button "Click to execute js", the modal does not open. Here is the plunker