Solve the equation for exact solutions over the interval 0,2∏
tan(squared)x - 3 = 0
The one you gave doesn't exist so I'm assuming you made a typo.
Add 3, then take the square root of both sides. Look on the unit circle to see which angles correspond to over the interval , which is pretty much the entire unit circle. Those points will be your solutions.
Why can't you have ? When I punch it into my calculator I get a number.
An imaginary number isn't on the x-axis. In order for that number to be a solution to the equation, the equation must intersect the x-axis at that point. Since that point doesn't exist on the x-axis when y = 0, then it is not a solution of the equation.
More precisely stands for "the set of the solutions is empty"
Originally Posted by Chris L T521
So our answer would just be an empty set,
is the set whose only member is the set . Saying that the set of the solutions of is means that for the equation is satisfied. In other words, . I guess we agree that this doesn't make sense at all. To say that the set of the solutions is empty, simply get rid of the two braces : the set of the solutions of is .