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

The general solution for 4sin(x)=3cos(x) is x=0.64350…+pin

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4sin(x)=3cos(x)

4 sin (x) = 3 cos (x)

x = 0.64350 \dots + πn

Degrees

x = 36.86989 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 sin (x) = 3 cos (x)

Rewrite using trig identities

4 sin (x) = 3 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

4 tan (x) = 3

4 tan (x) = 3

Divide both sides by

4

4 tan (x) = 3

Divide both sides by

4

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

Simplify

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

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

Apply trig inverse properties

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

General solutions for

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

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

x = arctan (\frac{3}{4}) + πn

x = arctan (\frac{3}{4}) + πn

Show solutions in decimal form

x = 0.64350 \dots + πn

2 cos^{2} (x) + sin (x) = 2

csc (x) = 4

csc (x) = 3

2 - 8 cos^{2} (t) = 0

cos (θ) + 1 = 1

What is the general solution for 4sin(x)=3cos(x) ?
The general solution for 4sin(x)=3cos(x) is x=0.64350…+pin