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

The general solution for 5cos(x)+2sin(x)=0 is x=-1.19028…+pin

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5cos(x)+2sin(x)=0

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

x = - 1.19028 \dots + πn

Degrees

x = - 68.19859 \dots^{\circ} + 18 0^{\circ} n

Solution steps

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

Rewrite using trig identities

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

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

5 + 2 tan (x) = 0

5 + 2 tan (x) = 0

Move

5

to the right side

5 + 2 tan (x) = 0

Subtract

5

from both sides

5 + 2 tan (x) - 5 = 0 - 5

Simplify

2 tan (x) = - 5

2 tan (x) = - 5

Divide both sides by

2

2 tan (x) = - 5

Divide both sides by

2

\frac{2 tan ( x )}{2} = \frac{- 5}{2}

Simplify

tan (x) = - \frac{5}{2}

tan (x) = - \frac{5}{2}

Apply trig inverse properties

tan (x) = - \frac{5}{2}

General solutions for

tan (x) = - \frac{5}{2}

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

x = arctan (- \frac{5}{2}) + πn

x = arctan (- \frac{5}{2}) + πn

Show solutions in decimal form

x = - 1.19028 \dots + πn

What is the general solution for 5cos(x)+2sin(x)=0 ?
The general solution for 5cos(x)+2sin(x)=0 is x=-1.19028…+pin