What is the general solution for sin(x)-4cos(x)=0 ?

The general solution for sin(x)-4cos(x)=0 is x=1.32581…+pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sin(x)-4cos(x)=0

sin (x) - 4 cos (x) = 0

x = 1.32581 \dots + πn

Degrees

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

Solution steps

sin (x) - 4 cos (x) = 0

Rewrite using trig identities

sin (x) - 4 cos (x) = 0

Divide both sides by

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

\frac{sin ( x ) - 4 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} - 4 = 0

Use the basic trigonometric identity:

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

tan (x) - 4 = 0

tan (x) - 4 = 0

Move

4

to the right side

tan (x) - 4 = 0

Add

4

to both sides

tan (x) - 4 + 4 = 0 + 4

Simplify

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

What is the general solution for sin(x)-4cos(x)=0 ?
The general solution for sin(x)-4cos(x)=0 is x=1.32581…+pin