What is the general solution for (sin(x))/(tan(x))=-0.375 ?

The general solution for (sin(x))/(tan(x))=-0.375 is x=1.95519…+2pin,x=-1.95519…+2pin

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(sin(x))/(tan(x))=-0.375

\frac{sin ( x )}{tan ( x )} = - 0.375

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

Degrees

x = 112.02431 \dots^{\circ} + 36 0^{\circ} n, x = - 112.02431 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{sin ( x )}{tan ( x )} = - 0.375

Subtract

- 0.375

from both sides

\frac{sin ( x )}{tan ( x )} + 0.375 = 0

Rewrite using trig identities

0.375 + \frac{sin ( x )}{tan ( x )}

Use the basic trigonometric identity:

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

= 0.375 + \frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}} = cos (x)

\frac{sin ( x )}{\frac{s i n ( x )}{c o s ( x )}}

Apply the fraction rule:

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

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

Cancel the common factor:

sin (x)

= cos (x)

= 0.375 + cos (x)

0.375 + cos (x) = 0

Move

0.375

to the right side

0.375 + cos (x) = 0

Subtract

0.375

from both sides

0.375 + cos (x) - 0.375 = 0 - 0.375

Simplify

cos (x) = - 0.375

cos (x) = - 0.375

Apply trig inverse properties

cos (x) = - 0.375

General solutions for

cos (x) = - 0.375

cos (x) = - a \Rightarrow x = arccos (- a) + 2 πn, x = - arccos (- a) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

x = arccos (- 0.375) + 2 πn, x = - arccos (- 0.375) + 2 πn

Show solutions in decimal form

x = 1.95519 \dots + 2 πn, x = - 1.95519 \dots + 2 πn

sin (2 x) = - sin (x), 0 \leq x \leq 2 π

2 sin (x) cos (x) + 2 sin (x) + cos (x) + 1 = 0

sin^{2} (θ) = 0

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

4 sin (x) cos (x) + 5 cos (x) = 0

What is the general solution for (sin(x))/(tan(x))=-0.375 ?
The general solution for (sin(x))/(tan(x))=-0.375 is x=1.95519…+2pin,x=-1.95519…+2pin