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

The general solution for pi/2 =2sin(x) is x=0.90333…+2pin,x=pi-0.90333…+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

pi/2 =2sin(x)

\frac{π}{2} = 2 sin (x)

x = 0.90333 \dots + 2 πn, x = π - 0.90333 \dots + 2 πn

Degrees

x = 51.75751 \dots^{\circ} + 36 0^{\circ} n, x = 128.24248 \dots^{\circ} + 36 0^{\circ} n

Solution steps

\frac{π}{2} = 2 sin (x)

Switch sides

2 sin (x) = \frac{π}{2}

Divide both sides by

2

2 sin (x) = \frac{π}{2}

Divide both sides by

2

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

Simplify

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

Simplify

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

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

Divide the numbers:

\frac{2}{2} = 1

= sin (x)

Simplify

\frac{\frac{π}{2}}{2} : \frac{π}{4}

\frac{\frac{π}{2}}{2}

Apply the fraction rule:

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

= \frac{π}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{π}{4}

sin (x) = \frac{π}{4}

sin (x) = \frac{π}{4}

sin (x) = \frac{π}{4}

Apply trig inverse properties

sin (x) = \frac{π}{4}

General solutions for

sin (x) = \frac{π}{4}

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

x = arcsin (\frac{π}{4}) + 2 πn, x = π - arcsin (\frac{π}{4}) + 2 πn

x = arcsin (\frac{π}{4}) + 2 πn, x = π - arcsin (\frac{π}{4}) + 2 πn

Show solutions in decimal form

x = 0.90333 \dots + 2 πn, x = π - 0.90333 \dots + 2 πn

What is the general solution for pi/2 =2sin(x) ?
The general solution for pi/2 =2sin(x) is x=0.90333…+2pin,x=pi-0.90333…+2pin