What is the general solution for sin(x)=-cos(x) ?

The general solution for sin(x)=-cos(x) is x=(3pi)/4+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)=-cos(x)

sin (x) = - cos (x)

x = \frac{3 π}{4} + πn

Degrees

x = 13 5^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = - cos (x)

Rewrite using trig identities

sin (x) = - cos (x)

Divide both sides by

cos (x), cos (x) \neq = 0

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

Simplify

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

Use the basic trigonometric identity:

\frac{sin ( x )}{cos ( x )} = tan (x)

tan (x) = - 1

tan (x) = - 1

General solutions for

tan (x) = - 1

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

x = \frac{3 π}{4} + πn

x = \frac{3 π}{4} + πn

tan (x) = \frac{1}{3}

sin (x) + 2 sin (x) cos (x) = 0

csc^{2} (x) - 2 = 0

2 sin^{2} (x) + cos (x) - 1 = 0

sin (4 x) = - 2 sin (2 x)

What is the general solution for sin(x)=-cos(x) ?
The general solution for sin(x)=-cos(x) is x=(3pi)/4+pin