What is the general solution for sin(x)-3cos(x)=0 ?

The general solution for sin(x)-3cos(x)=0 is x=1.24904…+pin

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sin(x)-3cos(x)=0

sin (x) - 3 cos (x) = 0

x = 1.24904 \dots + πn

Degrees

x = 71.56505 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) - 3 cos (x) = 0

Rewrite using trig identities

sin (x) - 3 cos (x) = 0

Divide both sides by

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

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

Simplify

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

Use the basic trigonometric identity:

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

tan (x) - 3 = 0

tan (x) - 3 = 0

Move

3

to the right side

tan (x) - 3 = 0

Add

3

to both sides

tan (x) - 3 + 3 = 0 + 3

Simplify

tan (x) = 3

tan (x) = 3

Apply trig inverse properties

tan (x) = 3

General solutions for

tan (x) = 3

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

x = arctan (3) + πn

x = arctan (3) + πn

Show solutions in decimal form

x = 1.24904 \dots + πn

cos (θ) = 1 + sin (θ)

4 sin^{2} (x) - 7 sin (x) - 2 = 0

cos (x) = - sin (2 x)

3 cot (x) - 3 = 0

cot (3 x) = \frac{3}{3}, 0 \leq x \leq 2 π

What is the general solution for sin(x)-3cos(x)=0 ?
The general solution for sin(x)-3cos(x)=0 is x=1.24904…+pin