What is the general solution for sin(x)-6cos(x)=0 ?

The general solution for sin(x)-6cos(x)=0 is x=1.40564…+pin

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sin(x)-6cos(x)=0

sin (x) - 6 cos (x) = 0

x = 1.40564 \dots + πn

Degrees

x = 80.53767 \dots^{\circ} + 18 0^{\circ} n

Solution steps

sin (x) - 6 cos (x) = 0

Rewrite using trig identities

sin (x) - 6 cos (x) = 0

Divide both sides by

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

\frac{sin ( x ) - 6 cos ( x )}{cos ( x )} = \frac{0}{cos ( x )}

Simplify

\frac{sin ( x )}{cos ( x )} - 6 = 0

Use the basic trigonometric identity:

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

tan (x) - 6 = 0

tan (x) - 6 = 0

Move

6

to the right side

tan (x) - 6 = 0

Add

6

to both sides

tan (x) - 6 + 6 = 0 + 6

Simplify

tan (x) = 6

tan (x) = 6

Apply trig inverse properties

tan (x) = 6

General solutions for

tan (x) = 6

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

x = arctan (6) + πn

x = arctan (6) + πn

Show solutions in decimal form

x = 1.40564 \dots + πn

What is the general solution for sin(x)-6cos(x)=0 ?
The general solution for sin(x)-6cos(x)=0 is x=1.40564…+pin