What is the general solution for cos(8x)=1 ?

The general solution for cos(8x)=1 is x=(pin)/4

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(8x)=1

cos (8 x) = 1

x = \frac{πn}{4}

Degrees

x = 0^{\circ} + 4 5^{\circ} n

Solution steps

cos (8 x) = 1

General solutions for

cos (8 x) = 1

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}

8 x = 0 + 2 πn

8 x = 0 + 2 πn

Solve

8 x = 0 + 2 πn : x = \frac{πn}{4}

8 x = 0 + 2 πn

0 + 2 πn = 2 πn

8 x = 2 πn

Divide both sides by

8

8 x = 2 πn

Divide both sides by

8

\frac{8 x}{8} = \frac{2 πn}{8}

Simplify

x = \frac{πn}{4}

x = \frac{πn}{4}

x = \frac{πn}{4}

cos^{4} (a) = 8 cos^{4} (a) - 8 cos^{2} (a) + 1

sin^{2} (a) - 4 sin (a) + 3 = 0

4 sin^{2} (x) - 4 cos (x) - 1 = 0

3 cos^{2} (x) + 2 cos (x) - 8 = 0

tan (a) + sec (a) = \frac{3}{2}

What is the general solution for cos(8x)=1 ?
The general solution for cos(8x)=1 is x=(pin)/4