What is the general solution for 4sin(x)=5cos(x) ?

The general solution for 4sin(x)=5cos(x) is x=0.89605…+pin

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4sin(x)=5cos(x)

4 sin (x) = 5 cos (x)

x = 0.89605 \dots + πn

Degrees

x = 51.34019 \dots^{\circ} + 18 0^{\circ} n

Solution steps

4 sin (x) = 5 cos (x)

Rewrite using trig identities

4 sin (x) = 5 cos (x)

Divide both sides by

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

\frac{4 sin ( x )}{cos ( x )} = \frac{5 cos ( x )}{cos ( x )}

Simplify

\frac{4 sin ( x )}{cos ( x )} = 5

Use the basic trigonometric identity:

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

4 tan (x) = 5

4 tan (x) = 5

Divide both sides by

4

4 tan (x) = 5

Divide both sides by

4

\frac{4 tan ( x )}{4} = \frac{5}{4}

Simplify

tan (x) = \frac{5}{4}

tan (x) = \frac{5}{4}

Apply trig inverse properties

tan (x) = \frac{5}{4}

General solutions for

tan (x) = \frac{5}{4}

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

x = arctan (\frac{5}{4}) + πn

x = arctan (\frac{5}{4}) + πn

Show solutions in decimal form

x = 0.89605 \dots + πn

What is the general solution for 4sin(x)=5cos(x) ?
The general solution for 4sin(x)=5cos(x) is x=0.89605…+pin