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} (x) - 3 cos (x) = 3

4 cos (x) = 3 + 8 cos (x)

sin^{2} (θ) - 3 sin (θ) = 0

cos^{2} (x) = \frac{1}{5}

- 3 cos (2 θ) + 5 = 7 sin (θ) + 5

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