What is the general solution for sin(x)= 1/3*cos(x) ?

The general solution for sin(x)= 1/3*cos(x) is x=0.32175…+pin

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sin(x)= 1/3*cos(x)

sin (x) = \frac{1}{3} \cdot cos (x)

x = 0.32175 \dots + πn

Degrees

x = 18.43494 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = \frac{1}{3} cos (x)

Rewrite using trig identities

sin (x) = \frac{1}{3} cos (x)

Divide both sides by

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

\frac{sin ( x )}{cos ( x )} = \frac{\frac{1}{3} cos ( x )}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} = \frac{1}{3}

Use the basic trigonometric identity:

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

tan (x) = \frac{1}{3}

tan (x) = \frac{1}{3}

Apply trig inverse properties

tan (x) = \frac{1}{3}

General solutions for

tan (x) = \frac{1}{3}

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

x = arctan (\frac{1}{3}) + πn

x = arctan (\frac{1}{3}) + πn

Show solutions in decimal form

x = 0.32175 \dots + πn

2 sin^{2} (x) - 1 = cos (x), 0 \leq x \leq 2 π

x, cos (3 y) = tan (2 x)

x, cos (x) = - \frac{26}{26}

6 cot (x) + 5 = - 1

11 csc (x) + 15 = 9 csc (x) + 19

What is the general solution for sin(x)= 1/3*cos(x) ?
The general solution for sin(x)= 1/3*cos(x) is x=0.32175…+pin