What is the general solution for sin(x)= 2/(sqrt(5)) ?

The general solution for sin(x)= 2/(sqrt(5)) is x=1.10714…+2pin,x=pi-1.10714…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(x)= 2/(sqrt(5))

sin (x) = \frac{2}{5}

x = 1.10714 \dots + 2 πn, x = π - 1.10714 \dots + 2 πn

Radians

x = 1.10714 \dots + 6.28318 \dots n, x = π - 1.10714 \dots + 6.28318 \dots n

Solution steps

sin (x) = \frac{2}{5}

Simplify

\frac{2}{5} : \frac{2 5}{5}

\frac{2}{5}

Multiply by the conjugate

\frac{5}{5}

= \frac{2 5}{5 5}

55 = 5

55

Apply radical rule:

a a = a

55 = 5

= 5

= \frac{2 5}{5}

sin (x) = \frac{2 5}{5}

Apply trig inverse properties

sin (x) = \frac{2 5}{5}

General solutions for

sin (x) = \frac{2 5}{5}

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

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

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

Show solutions in decimal form

x = 1.10714 \dots + 2 πn, x = π - 1.10714 \dots + 2 πn

csc (x) = 5

sec^{2} (x) + tan^{2} (x) - 1 = 0

tan^{2} (x) - 3 tan (x) = 0, 0 \leq x < 2 π

tan (θ) = 10

8 sin (θ) - 5 = 3 sin (θ)

What is the general solution for sin(x)= 2/(sqrt(5)) ?
The general solution for sin(x)= 2/(sqrt(5)) is x=1.10714…+2pin,x=pi-1.10714…+2pin