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

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

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sin(x)=-3cos(x)

sin (x) = - 3 cos (x)

x = - 1.24904 \dots + πn

Degrees

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

Solution steps

sin (x) = - 3 cos (x)

Rewrite using trig identities

sin (x) = - 3 cos (x)

Divide both sides by

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

\frac{sin ( x )}{cos ( x )} = \frac{- 3 cos ( x )}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} = - 3

Use the basic trigonometric identity:

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

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

- 2 sin^{2} (θ) + cos (θ) + 8 = 6

sin^{3} (t) = \frac{1}{8}

2 cos (t) \cdot sin (t) = cos (t)

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

csc (θ) = \frac{- 3}{5}

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