What is the general solution for sin(x)=(-3)/5 ?

The general solution for sin(x)=(-3)/5 is x=-0.64350…+2pin,x=pi+0.64350…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

sin(x)=(-3)/5

sin (x) = \frac{- 3}{5}

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

Degrees

x = - 36.86989 \dots^{\circ} + 36 0^{\circ} n, x = 216.86989 \dots^{\circ} + 36 0^{\circ} n

Solution steps

sin (x) = \frac{- 3}{5}

Apply the fraction rule:

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

sin (x) = - \frac{3}{5}

Apply trig inverse properties

sin (x) = - \frac{3}{5}

General solutions for

sin (x) = - \frac{3}{5}

sin (x) = - a \Rightarrow x = arcsin (- a) + 2 πn, x = π + arcsin (a) + 2 πn

x = arcsin (- \frac{3}{5}) + 2 πn, x = π + arcsin (\frac{3}{5}) + 2 πn

x = arcsin (- \frac{3}{5}) + 2 πn, x = π + arcsin (\frac{3}{5}) + 2 πn

Show solutions in decimal form

x = - 0.64350 \dots + 2 πn, x = π + 0.64350 \dots + 2 πn

2 cos (6 x) + 3 = 0

sin (\frac{π}{3} - x) = \frac{1}{2}

sin (x) = \frac{2}{3}

sin (x) + cos (x) = 1

2 sin^{2} (x) - sin (x) - 1 = 0, 0^{\circ} \leq x \leq 36 0^{\circ}

What is the general solution for sin(x)=(-3)/5 ?
The general solution for sin(x)=(-3)/5 is x=-0.64350…+2pin,x=pi+0.64350…+2pin