fillipeano said:Homework Statement
Find all solutions of the equation correct to two decimal places.
tan x = [itex]\sqrt{4 − x^2}[/itex]
Homework Equations
The Attempt at a Solution
I squared both sides, giving me tan^2x = 4 - x^2, but I don't know where to go from there.
When we are asked to find all solutions of an equation, it means we need to find all possible values for the variable(s) that make the equation true. These values are known as solutions or roots of the equation.
By finding all solutions of an equation, we can have a complete understanding of the relationship between the variables involved in the equation. This allows us to make accurate predictions and solve real-world problems.
To find all solutions of an equation, we typically use algebraic methods such as factoring, completing the square, or using the quadratic formula. We can also use graphical methods or numerical methods like iteration or interpolation.
When we say an answer is correct to two decimal places, it means that the number has been rounded to the nearest hundredth. This is represented by having two digits after the decimal point.
Yes, it is possible to have more than one solution for an equation. For example, a quadratic equation can have two real solutions, one real and one complex solution, or two complex solutions. It all depends on the nature of the equation and its solutions.