What is the general solution for -9sin(x)-9cos(x)=0 ?

The general solution for -9sin(x)-9cos(x)=0 is x=(3pi)/4+pin

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-9sin(x)-9cos(x)=0

- 9 sin (x) - 9 cos (x) = 0

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

- 9 sin (x) - 9 cos (x) = 0

Rewrite using trig identities

- 9 sin (x) - 9 cos (x) = 0

Divide both sides by

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

\frac{- 9 sin ( x ) - 9 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

- \frac{9 sin ( x )}{cos ( x )} - 9 = 0

Use the basic trigonometric identity:

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

- 9 tan (x) - 9 = 0

- 9 tan (x) - 9 = 0

Move

9

to the right side

- 9 tan (x) - 9 = 0

Add

9

to both sides

- 9 tan (x) - 9 + 9 = 0 + 9

Simplify

- 9 tan (x) = 9

- 9 tan (x) = 9

Divide both sides by

- 9

- 9 tan (x) = 9

Divide both sides by

- 9

\frac{- 9 tan ( x )}{- 9} = \frac{9}{- 9}

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

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

sin (x) = \frac{5}{2}

2 sin^{2} (θ) + 2 sin (θ) = 0

cos (3.7 x + 5.2) = 0

cos (x) = 96150182

What is the general solution for -9sin(x)-9cos(x)=0 ?
The general solution for -9sin(x)-9cos(x)=0 is x=(3pi)/4+pin