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

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

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3cos(x)=sin(x)

3 cos (x) = sin (x)

x = 1.24904 \dots + πn

Degrees

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

Solution steps

3 cos (x) = sin (x)

Rewrite using trig identities

3 cos (x) = sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 = tan (x)

Switch sides

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

sin^{2} (θ) - sin (θ) = cos^{2} (θ)

3 sin (x) = cos (x), - π \leq x \leq π

cos (x) = \frac{1999}{2000}

tan (13 5^{\circ} + x) = \frac{tan ( x ) - 1}{tan ( x ) + 1}

5 tan (x) + 5 = 0

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