What is the general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 ?

The general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 is x=-(1.13148…)/4+(pin)/4

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1032/3145 sin(4x)+2196/3145 cos(4x)=0

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

x = - \frac{1.13148 \dots}{4} + \frac{πn}{4}

Solution steps

\frac{1032}{3145} sin (4 x) + \frac{2196}{3145} cos (4 x) = 0

Rewrite using trig identities

\frac{1032 tan ( 4 x ) + 2196}{3145} = 0

Multiply both sides by

3145

1032 tan (4 x) + 2196 = 0

Move

2196

to the right side

1032 tan (4 x) = - 2196

Divide both sides by

1032

tan (4 x) = - \frac{183}{86}

Apply trig inverse properties

4 x = arctan (- \frac{183}{86}) + πn

Solve

4 x = arctan (- \frac{183}{86}) + πn : x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

x = - \frac{arctan ( \frac{183}{86} )}{4} + \frac{πn}{4}

Show solutions in decimal form

x = - \frac{1.13148 \dots}{4} + \frac{πn}{4}

6 - 2 sin (θ) - 8 sin^{2} (θ) = 0

cos (2 θ) = cos (3 θ)

θ, 2 sin (θ) = 1.5

cos (θ) = - 2109

x, cos (x) (cos (x) - sin (x)) = 0

What is the general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 ?
The general solution for 1032/3145 sin(4x)+2196/3145 cos(4x)=0 is x=-(1.13148…)/4+(pin)/4