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

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

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3cos(x)=5sin(x)

3 cos (x) = 5 sin (x)

x = 0.54041 \dots + πn

Degrees

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

Solution steps

3 cos (x) = 5 sin (x)

Rewrite using trig identities

3 cos (x) = 5 sin (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

3 = 5 tan (x)

Switch sides

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

4 cos (x) = 3 sin (x)

cos (π x) = 0, 0 \leq x \leq 2 π

cos (2 x - 1 5^{\circ}) = - sin (6 0^{\circ} - 3 x)

4 sin^{2} (x) - cos (x) - 1 = 0

tan (\frac{θ}{2} - \frac{π}{4}) = 1, 0 \leq θ < 2 π

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