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

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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

2 sin (x) + 53 = 63

- 5 \cdot cos (x) - 8.6602500000000 \dots \cdot sin (x) = - 5

y, cos (x) + cos (y) + cos (z) = 0

cos (x) = \frac{2}{5}

tan (\frac{x}{2} - \frac{π}{4}) = 3

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