What are the lowest possible values of the two terms on the left? How can they add to -3?utkarshakash said:Homework Statement
If [sinx]+[√2 cosx]=-3, x belongs to [0,2∏] (where [.] denotes the greatest integer function) then x belongs to
1)[5∏/4,2∏]
2)(5∏/4,2∏)
3)(∏,5∏/4)
4)[∏,5∏/4]
The Attempt at a Solution
If I put x=5∏/4, LHS=-2 which does not satisfy. 2∏ and ∏ also does not satisfy.So the answer must be either 2) or 3). Is there any better way other than putting the values one by one and checking?
haruspex said:What are the lowest possible values of the two terms on the left? How can they add to -3?
Finding roots of a trigonometric equation refers to determining the values of the variable that make the equation true. In other words, it is the process of finding the solutions or values of the variable that satisfy the given trigonometric equation.
The process of finding roots of a trigonometric equation depends on the specific equation and may involve using algebraic manipulation, trigonometric identities, and properties of trigonometric functions. It may also require the use of a calculator or graphing software to approximate the solutions.
Yes, a trigonometric equation can have multiple roots or solutions. This is because trigonometric functions are periodic, meaning they repeat their values after a certain interval. Therefore, there can be multiple values of the variable that satisfy the equation.
An extraneous root is a solution that does not satisfy the original equation. This can occur when the equation has been manipulated in a way that introduces additional solutions. It is important to always check the solutions in the original equation to ensure they are valid.
Yes, there are a few special cases to consider when finding roots of trigonometric equations. These include equations with multiple angles, equations involving inverse trigonometric functions, and equations with restrictions on the domain. It is important to be familiar with these cases and their solutions when solving trigonometric equations.