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

The general solution for 5sin(x)+3cos(x)=0 is x=-0.54041…+pin

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5sin(x)+3cos(x)=0

5 sin (x) + 3 cos (x) = 0

x = - 0.54041 \dots + πn

Degrees

x = - 30.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

5 sin (x) + 3 cos (x) = 0

Rewrite using trig identities

5 sin (x) + 3 cos (x) = 0

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

5 tan (x) + 3 = 0

5 tan (x) + 3 = 0

Move

3

to the right side

5 tan (x) + 3 = 0

Subtract

3

from both sides

5 tan (x) + 3 - 3 = 0 - 3

Simplify

5 tan (x) = - 3

5 tan (x) = - 3

Divide both sides by

5

5 tan (x) = - 3

Divide both sides by

5

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (- \frac{3}{5}) + πn

x = arctan (- \frac{3}{5}) + πn

Show solutions in decimal form

x = - 0.54041 \dots + πn

3 cos (x) csc (x) = 2 cos (x)

sin (2 x) = - \frac{2}{2}

sin (x) = 0, 0 \leq x < 2 π

sec^{2} (x) = (3 + 1) tan (x) - 3 + 1

sin (z) = 100

What is the general solution for 5sin(x)+3cos(x)=0 ?
The general solution for 5sin(x)+3cos(x)=0 is x=-0.54041…+pin