What is the general solution for 3sin(x)-4cos(x)=0 ?

The general solution for 3sin(x)-4cos(x)=0 is x=0.92729…+pin

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3sin(x)-4cos(x)=0

3 sin (x) - 4 cos (x) = 0

x = 0.92729 \dots + πn

Degrees

x = 53.13010 \dots^{\circ} + 18 0^{\circ} n

Solution steps

3 sin (x) - 4 cos (x) = 0

Rewrite using trig identities

3 sin (x) - 4 cos (x) = 0

Divide both sides by

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

\frac{3 sin ( x ) - 4 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{3 sin ( x )}{cos ( x )} - 4 = 0

Use the basic trigonometric identity:

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

3 tan (x) - 4 = 0

3 tan (x) - 4 = 0

Move

4

to the right side

3 tan (x) - 4 = 0

Add

4

to both sides

3 tan (x) - 4 + 4 = 0 + 4

Simplify

3 tan (x) = 4

3 tan (x) = 4

Divide both sides by

3

3 tan (x) = 4

Divide both sides by

3

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{4}{3}) + πn

x = arctan (\frac{4}{3}) + πn

Show solutions in decimal form

x = 0.92729 \dots + πn

sin (θ) = \frac{1}{4}, 0^{\circ} < θ < 9 0^{\circ}

sin (90 - 2 x) = cos (9 0^{\circ} - x)

tan (\frac{x}{2}) = - 0.39

4 sin (3 x) - 1 = 0

\frac{7}{4} cos (3 θ) - 1 = 0

What is the general solution for 3sin(x)-4cos(x)=0 ?
The general solution for 3sin(x)-4cos(x)=0 is x=0.92729…+pin