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

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

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solvefor x,sin(x)=3cos(x)

solve for

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

x, 1.12 = 0.04 sin (x)

sin (2 x) = - 0.8

cos (2 x - \frac{π}{5}) = 0

cos (a) = sin (a + 3 0^{\circ})

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

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