What is the general solution for -cos(x)-sin(x)=0 ?

The general solution for -cos(x)-sin(x)=0 is x=(3pi)/4+pin

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

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

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

\frac{- cos ( x ) - sin ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

- 1 - \frac{sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

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

- 1 - tan (x) = 0

- 1 - tan (x) = 0

Move

1

to the right side

- 1 - tan (x) = 0

Add

1

to both sides

- 1 - tan (x) + 1 = 0 + 1

Simplify

- tan (x) = 1

- tan (x) = 1

Divide both sides by

- 1

- tan (x) = 1

Divide both sides by

- 1

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

Simplify

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

sin (x) = - \frac{1}{6}

sin (θ) = \frac{8}{14}

sin (θ) = \frac{8}{10}

- 10 = 8 tan (x) + 6

- 4 sin (2 θ) = 5 cos (2 θ), 0^{\circ} \leq 2 θ < 72 0^{\circ}

What is the general solution for -cos(x)-sin(x)=0 ?
The general solution for -cos(x)-sin(x)=0 is x=(3pi)/4+pin