What is the general solution for -6sin(x)-6cos(x)=0 ?

The general solution for -6sin(x)-6cos(x)=0 is x=(3pi)/4+pin

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-6sin(x)-6cos(x)=0

- 6 sin (x) - 6 cos (x) = 0

x = \frac{3 π}{4} + πn

Degrees

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

Solution steps

- 6 sin (x) - 6 cos (x) = 0

Rewrite using trig identities

- 6 sin (x) - 6 cos (x) = 0

Divide both sides by

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

\frac{- 6 sin ( x ) - 6 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

- \frac{6 sin ( x )}{cos ( x )} - 6 = 0

Use the basic trigonometric identity:

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

- 6 tan (x) - 6 = 0

- 6 tan (x) - 6 = 0

Move

6

to the right side

- 6 tan (x) - 6 = 0

Add

6

to both sides

- 6 tan (x) - 6 + 6 = 0 + 6

Simplify

- 6 tan (x) = 6

- 6 tan (x) = 6

Divide both sides by

- 6

- 6 tan (x) = 6

Divide both sides by

- 6

\frac{- 6 tan ( x )}{- 6} = \frac{6}{- 6}

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 (4 x) - sin (2 x) = cos (3 x)

sin (x) = 0.7392

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

3 + 2 sin (x) = 0

tan (x) = \frac{6}{4}

What is the general solution for -6sin(x)-6cos(x)=0 ?
The general solution for -6sin(x)-6cos(x)=0 is x=(3pi)/4+pin