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

The general solution for sin(x)=5cos(x) is x=1.37340…+pin

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sin(x)=5cos(x)

sin (x) = 5 cos (x)

x = 1.37340 \dots + πn

Degrees

x = 78.69006 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = 5 cos (x)

Rewrite using trig identities

sin (x) = 5 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) = 5

tan (x) = 5

Apply trig inverse properties

tan (x) = 5

General solutions for

tan (x) = 5

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

x = arctan (5) + πn

x = arctan (5) + πn

Show solutions in decimal form

x = 1.37340 \dots + πn

cos (5 x) - cos (x) = sin (5 x) - sin (x)

\frac{1}{4} = sin (x)

sin (x) cos (x) - \frac{3}{2} sin (x) = 0

43 = arcsin (\frac{1}{x})

tan (x) sin (x) = tan (x)

What is the general solution for sin(x)=5cos(x) ?
The general solution for sin(x)=5cos(x) is x=1.37340…+pin