\text{Solve for }x of \sin(x)-\cos(x)=0

x=\frac{\pi }{4}+k\pi ,k \in \mathbb{Z}

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Question :

sin(x)-cos(x)=0

Solve the equation

x = \frac{π}{4} + kπ, k \in Z

Alternative Form

x = 4 5^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

x \approx 0.785398 + kπ, k \in Z

Evaluate

sin (x) - cos (x) = 0

Move the expression to the right side

- cos (x) = 0 - sin (x)

Subtract the terms

- cos (x) = - sin (x)

Divide both sides

\frac{- cos ( x )}{sin ( x )} = - 1

Divide the terms

More Steps

Evaluate

\frac{- cos ( x )}{sin ( x )}

Use \frac{- a}{b} = \frac{a}{- b} = - \frac{a}{b} to rewrite the fraction

- \frac{cos ( x )}{sin ( x )}

Rewrite the expression

- sin^{- 1} (x) cos (x)

Rewrite the expression

- cot (x)

- cot (x) = - 1

Multiply both sides of the equation by - 1

- cot (x) (- 1) = - (- 1)

Calculate

cot (x) = - (- 1)

Multiplying or dividing an even number of negative terms equals a positive

cot (x) = 1

Use the inverse trigonometric function

x = arccot (1)

Calculate

x = \frac{π}{4}

Solution

x = \frac{π}{4} + kπ, k \in Z

Alternative Form

x = 4 5^{\circ} + 18 0^{\circ} k, k \in Z

Alternative Form

x \approx 0.785398 + kπ, k \in Z

Show Solution

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Frequently Asked Questions

$Solve for x$ of $\sin(x)-\cos(x)=0$

$x = \frac{π}{4} + kπ, k \in Z$

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English

sin(x)-cos(x)=0

Solve the equation

Graph

Frequently Asked Questions

Solve for x of \(\sin(x)-\cos(x)=0\)

$Solve for x$ of \(\sin(x)-\cos(x)=0\)