What is the general solution for cos(a)=-1/(sqrt(2)) ?

The general solution for cos(a)=-1/(sqrt(2)) is a=(3pi)/4+2pin,a=(5pi)/4+2pin

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(a)=-1/(sqrt(2))

cos (a) = - \frac{1}{2}

a = \frac{3 π}{4} + 2 πn, a = \frac{5 π}{4} + 2 πn

Solution steps

cos (a) = - \frac{1}{2}

Simplify

- \frac{1}{2} : - \frac{2}{2}

- \frac{1}{2}

Multiply by the conjugate

\frac{2}{2}

= - \frac{1 \cdot 2}{2 2}

1 \cdot 2 = 2

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

cos (a) = - \frac{2}{2}

General solutions for

cos (a) = - \frac{2}{2}

cos (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} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{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} cos (x) - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2} 0 \frac{1}{2} \frac{2}{2} \frac{3}{2}

a = \frac{3 π}{4} + 2 πn, a = \frac{5 π}{4} + 2 πn

a = \frac{3 π}{4} + 2 πn, a = \frac{5 π}{4} + 2 πn

- 4 cos (2 x) + 4 sin (x) = 0

6 sin (θ) = 1

- 5 sin (y) = 0

2 cos (\frac{3 x - π}{6}) + 1 = 0, 0 < x < 2 π

sin (α) = - 1

What is the general solution for cos(a)=-1/(sqrt(2)) ?
The general solution for cos(a)=-1/(sqrt(2)) is a=(3pi)/4+2pin,a=(5pi)/4+2pin