# Cos(x)+sin(x) = 0, Find all values?

• DrummingAtom
In summary, the solution to the equation Cos(x)+sin(x) = 0 is 3pi/4, and you can obtain infinite other values by adding pi to it. However, when using a calculator, a small error may occur, but it does not affect the overall solution.
DrummingAtom

## Homework Statement

Cos(x)+sin(x) = 0, Find all values?

## The Attempt at a Solution

I've found the first solution, which is 3pi/4 and I figured I can just add pi to that value over and over to obtain the infinite other values. But when I punch it in my calculator it's coming up that cos(7pi/4)+sin(7pi/4) = 0.000000000021

I'm not sure if this is a calculator computation issue or I'm doing something wrong.. Thanks for any help.

DrummingAtom said:

## Homework Statement

Cos(x)+sin(x) = 0, Find all values?

## The Attempt at a Solution

I've found the first solution, which is 3pi/4 and I figured I can just add pi to that value over and over to obtain the infinite other values. But when I punch it in my calculator it's coming up that cos(7pi/4)+sin(7pi/4) = 0.000000000021

I'm not sure if this is a calculator computation issue or I'm doing something wrong.. Thanks for any help.
No, you're not doing anything wrong. This error is due to the calculator.

## 1. What is the general solution to the equation Cos(x)+sin(x) = 0?

The general solution to this equation is x = (2n+1)π/4, where n is an integer.

## 2. How do you determine the specific values of x that satisfy the equation Cos(x)+sin(x) = 0?

To determine the specific values of x, you can use a trigonometric identity such as Cos(x) = -sin(x) to rewrite the equation as -sin(x)+sin(x)=0. This simplifies to 0=0, which is always true. Therefore, any value of x will satisfy the equation.

## 3. Are there any restrictions on the values of x for which Cos(x)+sin(x) = 0?

No, there are no restrictions on the values of x for which Cos(x)+sin(x) = 0. Any value of x will satisfy the equation.

## 4. How many solutions does the equation Cos(x)+sin(x) = 0 have?

This equation has an infinite number of solutions because any value of x will satisfy the equation.

## 5. Can this equation be solved algebraically?

No, this equation cannot be solved algebraically. It can only be solved by using a trigonometric identity to rewrite the equation or by graphing it to find the solutions visually.

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