What is the general solution for sin(x)=(-(6))/((7)cos(x)) ?

The general solution for sin(x)=(-(6))/((7)cos(x)) is No Solution for x\in\mathbb{R}

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sin(x)=(-(6))/((7)cos(x))

sin (x) = \frac{- ( 6 )}{( 7 ) cos ( x )}

No Solution for x \in R

Solution steps

sin (x) = \frac{- ( 6 )}{( 7 ) cos ( x )}

Subtract

\frac{- 6}{7 cos ( x )}

from both sides

sin (x) + \frac{6}{7 cos ( x )} = 0

Simplify

sin (x) + \frac{6}{7 cos ( x )} : \frac{7 sin ( x ) cos ( x ) + 6}{7 cos ( x )}

\frac{7 sin ( x ) cos ( x ) + 6}{7 cos ( x )} = 0

\frac{f ( x )}{g ( x )} = 0 \Rightarrow f (x) = 0

7 sin (x) cos (x) + 6 = 0

Rewrite using trig identities

6 + 7 \cdot \frac{sin ( 2 x )}{2} = 0

Move

6

to the right side

7 \cdot \frac{sin ( 2 x )}{2} = - 6

Refine

7 \cdot \frac{sin ( 2 x )}{2} : \frac{7 sin ( 2 x )}{2}

\frac{7 sin ( 2 x )}{2} = - 6

Multiply both sides by

2

7 sin (2 x) = - 12

Divide both sides by

7

sin (2 x) = - \frac{12}{7}

- 1 \leq sin (x) \leq 1

No Solution for x \in R

5^{2} = 8^{2} - (11.85)^{2} - 2 (8) (11.85) (cos (A))

2 + 2 sin (θ) = 4

- 4 sin (8 x) = 0

- sin (x) + 2 cos (x) = 0

\frac{sin ( θ )}{140} = \frac{sin ( 11 0 ^{\circ} )}{622}

What is the general solution for sin(x)=(-(6))/((7)cos(x)) ?
The general solution for sin(x)=(-(6))/((7)cos(x)) is No Solution for x\in\mathbb{R}