What is the general solution for sin(2x)=-5cos(2x) ?

The general solution for sin(2x)=-5cos(2x) is x=-(1.37340…)/2+(pin)/2

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sin(2x)=-5cos(2x)

sin (2 x) = - 5 cos (2 x)

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

Solution steps

sin (2 x) = - 5 cos (2 x)

Rewrite using trig identities

tan (2 x) = - 5

Apply trig inverse properties

2 x = arctan (- 5) + πn

Solve

2 x = arctan (- 5) + πn : x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

x = - \frac{arctan ( 5 )}{2} + \frac{πn}{2}

Show solutions in decimal form

x = - \frac{1.37340 \dots}{2} + \frac{πn}{2}

tan (x) cot (x) = sec (x) csc (x)

4 sin (x) = cos (x) - 2

sin (θ) = 1 - cos (θ)

cos (θ) - 2 sin (θ) cos (θ) = 0

x, cos (x y) = sin (x + y)

What is the general solution for sin(2x)=-5cos(2x) ?
The general solution for sin(2x)=-5cos(2x) is x=-(1.37340…)/2+(pin)/2