What is the general solution for -(10cos(θ))/(sqrt(3))=10sin(θ) ?

The general solution for -(10cos(θ))/(sqrt(3))=10sin(θ) is θ=(5pi)/6+pin

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Popular >

-(10cos(θ))/(sqrt(3))=10sin(θ)

Solution

- \frac{10 cos ( θ )}{3} = 10 sin (θ)

Solution

θ = \frac{5 π}{6} + πn

Degrees

θ = 15 0^{\circ} + 18 0^{\circ} n

Solution steps

- \frac{10 cos ( θ )}{3} = 10 sin (θ)

Rewrite using trig identities

- \frac{10 cos ( θ )}{3} = 10 sin (θ)

Divide both sides by

cos (θ), cos (θ) \neq = 0

\frac{- \frac{10 c o s ( θ )}{3}}{cos ( θ )} = \frac{10 sin ( θ )}{cos ( θ )}

Simplify

- \frac{10}{3} = \frac{10 sin ( θ )}{cos ( θ )}

Use the basic trigonometric identity:

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

- \frac{10}{3} = 10 tan (θ)

Switch sides

10 tan (θ) = - \frac{10}{3}

10 tan (θ) = - \frac{10}{3}

Divide both sides by

10

10 tan (θ) = - \frac{10}{3}

Divide both sides by

10

\frac{10 tan ( θ )}{10} = \frac{- \frac{10}{3}}{10}

Simplify

\frac{10 tan ( θ )}{10} = \frac{- \frac{10}{3}}{10}

Simplify

\frac{10 tan ( θ )}{10} : tan (θ)

\frac{10 tan ( θ )}{10}

Divide the numbers:

\frac{10}{10} = 1

= tan (θ)

Simplify

\frac{- \frac{10}{3}}{10} : - \frac{3}{3}

\frac{- \frac{10}{3}}{10}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{\frac{10}{3}}{10}

Apply the fraction rule:

\frac{\frac{b}{c}}{a} = \frac{b}{c \cdot a}

\frac{\frac{10}{3}}{10} = \frac{10}{3 \cdot 10}

= - \frac{10}{3 \cdot 10}

Divide the numbers:

\frac{10}{10} = 1

= - \frac{1}{3}

Rationalize

- \frac{1}{3} : - \frac{3}{3}

- \frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= - \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= - \frac{3}{3}

= - \frac{3}{3}

tan (θ) = - \frac{3}{3}

tan (θ) = - \frac{3}{3}

tan (θ) = - \frac{3}{3}

General solutions for

tan (θ) = - \frac{3}{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}

θ = \frac{5 π}{6} + πn

θ = \frac{5 π}{6} + πn

Graph

Popular Examples

11tan(c)+6=3tan(c)+6

11 tan (c) + 6 = 3 tan (c) + 6

sin(x)=(-11)/(11sqrt(2))

sin (x) = \frac{- 11}{11 2}

tan(x)= 43/45

tan (x) = \frac{43}{45}

3tan^2(x)+5tan(x)+2=0

3 tan^{2} (x) + 5 tan (x) + 2 = 0

sin(2x+pi/3)=-(sqrt(3))/2

sin (2 x + \frac{π}{3}) = - \frac{3}{2}

Frequently Asked Questions (FAQ)

What is the general solution for -(10cos(θ))/(sqrt(3))=10sin(θ) ?
The general solution for -(10cos(θ))/(sqrt(3))=10sin(θ) is θ=(5pi)/6+pin