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

Solution steps

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

Rewrite using trig identities

tan (x) - 3 = 0

Move

3

to the right side

tan (x) = 3

Apply trig inverse properties

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