What is the general solution for sin(a)+sqrt(3)cos(a)=0 ?

The general solution for sin(a)+sqrt(3)cos(a)=0 is a=(2pi)/3+pin

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sin(a)+sqrt(3)cos(a)=0

sin (a) + 3 cos (a) = 0

a = \frac{2 π}{3} + πn

Degrees

a = 12 0^{\circ} + 18 0^{\circ} n

Solution steps

sin (a) + 3 cos (a) = 0

Rewrite using trig identities

sin (a) + 3 cos (a) = 0

Divide both sides by

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

\frac{sin ( a ) + 3 cos ( a )}{cos ( a )} = \frac{0}{cos ( a )}

Simplify

\frac{sin ( a )}{cos ( a )} + 3 = 0

Use the basic trigonometric identity:

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

tan (a) + 3 = 0

tan (a) + 3 = 0

Move

3

to the right side

tan (a) + 3 = 0

Subtract

3

from both sides

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

Simplify

tan (a) = - 3

tan (a) = - 3

General solutions for

tan (a) = - 3

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

a = \frac{2 π}{3} + πn

a = \frac{2 π}{3} + πn

22 cos (θ) + 3 = 5

sin (a) cos (a) = 1

sin (2 π x) = 0

sin (5 x) = 1

tan (θ) = 2.2

What is the general solution for sin(a)+sqrt(3)cos(a)=0 ?
The general solution for sin(a)+sqrt(3)cos(a)=0 is a=(2pi)/3+pin