What is the general solution for 20/3 sin(10x)+5cos(10x)=0 ?

The general solution for 20/3 sin(10x)+5cos(10x)=0 is x=-(0.64350…)/(10)+(pin)/(10)

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20/3 sin(10x)+5cos(10x)=0

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

x = - \frac{0.64350 \dots}{10} + \frac{πn}{10}

Solution steps

\frac{20}{3} sin (10 x) + 5 cos (10 x) = 0

Rewrite using trig identities

\frac{20 tan ( 10 x )}{3} + 5 = 0

Move

5

to the right side

\frac{20 tan ( 10 x )}{3} = - 5

Multiply both sides by

3

20 tan (10 x) = - 15

Divide both sides by

20

tan (10 x) = - \frac{3}{4}

Apply trig inverse properties

10 x = arctan (- \frac{3}{4}) + πn

Solve

10 x = arctan (- \frac{3}{4}) + πn : x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

x = - \frac{arctan ( \frac{3}{4} )}{10} + \frac{πn}{10}

Show solutions in decimal form

x = - \frac{0.64350 \dots}{10} + \frac{πn}{10}

5 sin^{2} (x) = 0

(\frac{( 1 - sin ^{2} ( x ) )}{( 1 + 2 \cdot sin ^{2} ( x ) )}) = 0.4

cos (3 x + \frac{π}{4}) = - \frac{3}{2}

1 = cos (\frac{π}{64} \cdot t^{2})

sin (x) - \frac{1}{4} = 0

What is the general solution for 20/3 sin(10x)+5cos(10x)=0 ?
The general solution for 20/3 sin(10x)+5cos(10x)=0 is x=-(0.64350…)/(10)+(pin)/(10)