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

The general solution for sin(a)=(sqrt(2))/2 is a= pi/4+2pin,a=(3pi)/4+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sin(a)=(sqrt(2))/2

sin (a) = \frac{2}{2}

a = \frac{π}{4} + 2 πn, a = \frac{3 π}{4} + 2 πn

Degrees

a = 4 5^{\circ} + 36 0^{\circ} n, a = 13 5^{\circ} + 36 0^{\circ} n

Solution steps

sin (a) = \frac{2}{2}

General solutions for

sin (a) = \frac{2}{2}

sin (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

a = \frac{π}{4} + 2 πn, a = \frac{3 π}{4} + 2 πn

a = \frac{π}{4} + 2 πn, a = \frac{3 π}{4} + 2 πn

sin^{2} (x) - cos (x) = 1

cos^{2} (x) + 2 sin (x) + 2 = 0

2 sin^{2} (2 x + π) - sin (2 x + π) - 1 = 0

cos (x) = 9

sec (θ) = \frac{3}{5}

What is the general solution for sin(a)=(sqrt(2))/2 ?
The general solution for sin(a)=(sqrt(2))/2 is a= pi/4+2pin,a=(3pi)/4+2pin