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

The general solution for sin(x)=4cos(x) is x=1.32581…+pin

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sin(x)=4cos(x)

sin (x) = 4 cos (x)

x = 1.32581 \dots + πn

Degrees

x = 75.96375 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) = 4 cos (x)

Rewrite using trig identities

sin (x) = 4 cos (x)

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) = 4

tan (x) = 4

Apply trig inverse properties

tan (x) = 4

General solutions for

tan (x) = 4

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

x = arctan (4) + πn

x = arctan (4) + πn

Show solutions in decimal form

x = 1.32581 \dots + πn

7 cos (x) = 0

sin (θ) = \frac{3 13}{13}, sec (θ)

sin (y) = \frac{1}{2}

3 sin^{2} (x) = 5 sin (x) + 2

sin (x) + cos (x) = 0, - \frac{π}{2} \leq x \leq π

What is the general solution for sin(x)=4cos(x) ?
The general solution for sin(x)=4cos(x) is x=1.32581…+pin