What is the general solution for sin(3x)=2.5cos(3x) ?

The general solution for sin(3x)=2.5cos(3x) is x=(1.19028…)/3+(pin)/3

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sin(3x)=2.5cos(3x)

sin (3 x) = 2.5 cos (3 x)

x = \frac{1.19028 \dots}{3} + \frac{πn}{3}

Degrees

x = 22.73286 \dots^{\circ} + 6 0^{\circ} n

Solution steps

sin (3 x) = 2.5 cos (3 x)

Rewrite using trig identities

sin (3 x) = 2.5 cos (3 x)

Divide both sides by

cos (3 x), cos (3 x) \neq = 0

\frac{sin ( 3 x )}{cos ( 3 x )} = \frac{2.5 cos ( 3 x )}{cos ( 3 x )}

Simplify

\frac{sin ( 3 x )}{cos ( 3 x )} = 2.5

Use the basic trigonometric identity:

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

tan (3 x) = 2.5

tan (3 x) = 2.5

Apply trig inverse properties

tan (3 x) = 2.5

General solutions for

tan (3 x) = 2.5

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

3 x = arctan (2.5) + πn

3 x = arctan (2.5) + πn

Solve

3 x = arctan (2.5) + πn : x = \frac{arctan ( 2.5 )}{3} + \frac{πn}{3}

3 x = arctan (2.5) + πn

Divide both sides by

3

3 x = arctan (2.5) + πn

Divide both sides by

3

\frac{3 x}{3} = \frac{arctan ( 2.5 )}{3} + \frac{πn}{3}

Simplify

x = \frac{arctan ( 2.5 )}{3} + \frac{πn}{3}

x = \frac{arctan ( 2.5 )}{3} + \frac{πn}{3}

x = \frac{arctan ( 2.5 )}{3} + \frac{πn}{3}

Show solutions in decimal form

x = \frac{1.19028 \dots}{3} + \frac{πn}{3}

sin (x) + cos (x) = \frac{3}{5}

sec (\frac{5 θ}{4}) = 2, 0 \leq θ \leq 2 π

3 cot (θ) - 1 = - cot^{2} (θ)

4 cos (x) - 23 = 0

tan^{3} (x) - tan^{2} (x) - 3 tan (x) + 3 = 0

What is the general solution for sin(3x)=2.5cos(3x) ?
The general solution for sin(3x)=2.5cos(3x) is x=(1.19028…)/3+(pin)/3