What is the general solution for 6sin(x)+5cos(x)=0 ?

The general solution for 6sin(x)+5cos(x)=0 is x=-0.69473…+pin

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6sin(x)+5cos(x)=0

6 sin (x) + 5 cos (x) = 0

x = - 0.69473 \dots + πn

Degrees

x = - 39.80557 \dots^{\circ} + 18 0^{\circ} n

Solution steps

6 sin (x) + 5 cos (x) = 0

Rewrite using trig identities

6 sin (x) + 5 cos (x) = 0

Divide both sides by

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

\frac{6 sin ( x ) + 5 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{6 sin ( x )}{cos ( x )} + 5 = 0

Use the basic trigonometric identity:

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

6 tan (x) + 5 = 0

6 tan (x) + 5 = 0

Move

5

to the right side

6 tan (x) + 5 = 0

Subtract

5

from both sides

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

Simplify

6 tan (x) = - 5

6 tan (x) = - 5

Divide both sides by

6

6 tan (x) = - 5

Divide both sides by

6

\frac{6 tan ( x )}{6} = \frac{- 5}{6}

Simplify

tan (x) = - \frac{5}{6}

tan (x) = - \frac{5}{6}

Apply trig inverse properties

tan (x) = - \frac{5}{6}

General solutions for

tan (x) = - \frac{5}{6}

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

x = arctan (- \frac{5}{6}) + πn

x = arctan (- \frac{5}{6}) + πn

Show solutions in decimal form

x = - 0.69473 \dots + πn

2 cos^{2} (x) - 5 cos (x) + 3 = 0

2 sin^{3} (x) = 0

csc (x) = - 2

6 cos (A) + 18 = 0

csc (θ) = \frac{5}{2}

What is the general solution for 6sin(x)+5cos(x)=0 ?
The general solution for 6sin(x)+5cos(x)=0 is x=-0.69473…+pin