What is the general solution for (cos(x)+5sin(x))/(2-3)=0 ?

The general solution for (cos(x)+5sin(x))/(2-3)=0 is x=-0.19739…+pin

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(cos(x)+5sin(x))/(2-3)=0

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

x = - 0.19739 \dots + πn

Degrees

x = - 11.30993 \dots^{\circ} + 18 0^{\circ} n

Solution steps

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

Rewrite using trig identities

\frac{cos ( x ) + 5 sin ( x )}{2 - 3} = 0

Divide both sides by

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

\frac{\frac{c o s ( x ) + 5 s i n ( x )}{2 - 3}}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

- 1 - \frac{5 sin ( x )}{cos ( x )} = 0

Use the basic trigonometric identity:

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

- 1 - 5 tan (x) = 0

- 1 - 5 tan (x) = 0

Move

1

to the right side

- 1 - 5 tan (x) = 0

Add

1

to both sides

- 1 - 5 tan (x) + 1 = 0 + 1

Simplify

- 5 tan (x) = 1

- 5 tan (x) = 1

Divide both sides by

- 5

- 5 tan (x) = 1

Divide both sides by

- 5

\frac{- 5 tan ( x )}{- 5} = \frac{1}{- 5}

Simplify

tan (x) = - \frac{1}{5}

tan (x) = - \frac{1}{5}

Apply trig inverse properties

tan (x) = - \frac{1}{5}

General solutions for

tan (x) = - \frac{1}{5}

tan (x) = - a \Rightarrow x = arctan (- a) + πn

x = arctan (- \frac{1}{5}) + πn

x = arctan (- \frac{1}{5}) + πn

Show solutions in decimal form

x = - 0.19739 \dots + πn

sin (y) = \frac{2}{3}

sin (a) = 0.6625

6 - 4 cos^{2} (x) - 9 sin (x) = 0

cos^{2} (x) + cos^{2} (3 x) = 1

tan (x) = \frac{16}{3}

What is the general solution for (cos(x)+5sin(x))/(2-3)=0 ?
The general solution for (cos(x)+5sin(x))/(2-3)=0 is x=-0.19739…+pin