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

Solution steps

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

Rewrite using trig identities

tan (x) + 3 = 0

Move

3

to the right side

tan (x) = - 3

Apply trig inverse properties

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