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

The general solution for sin(x)+3cos(x)=0 is x=-1.24904…+pin

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sin(x)+3cos(x)=0

sin (x) + 3 cos (x) = 0

x = - 1.24904 \dots + πn

Degrees

x = - 71.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) + 3 cos (x) = 0

Rewrite using trig identities

sin (x) + 3 cos (x) = 0

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) + 3 = 0

tan (x) + 3 = 0

Move

3

to the right side

tan (x) + 3 = 0

Subtract

3

from both sides

tan (x) + 3 - 3 = 0 - 3

Simplify

tan (x) = - 3

tan (x) = - 3

Apply trig inverse properties

tan (x) = - 3

General solutions for

tan (x) = - 3

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

x = arctan (- 3) + πn

x = arctan (- 3) + πn

Show solutions in decimal form

x = - 1.24904 \dots + πn

cos (x) = \frac{1}{csc ( x )}

- cot (2 x) = 0

cos (x) = \frac{π}{6}

3 cos (2 θ) + 6 = - 5 cos (θ) + 2

sin (3 x) cos (x) - sin (x) cos (3 x) = 0

What is the general solution for sin(x)+3cos(x)=0 ?
The general solution for sin(x)+3cos(x)=0 is x=-1.24904…+pin