What is the value of (cos(0)-sin(0))/(sqrt(3)) ?

The value of (cos(0)-sin(0))/(sqrt(3)) is (sqrt(3))/3

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

(cos(0)-sin(0))/(sqrt(3))

\frac{cos ( 0 ) - sin ( 0 )}{3}

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

\frac{cos ( 0 ) - sin ( 0 )}{3}

Use the following trivial identity:

cos (0) = 1

cos (0)

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}

= 1

Use the following trivial identity:

sin (0) = 0

sin (0)

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}

= 0

= \frac{1 - 0}{3}

Simplify

\frac{1 - 0}{3} : \frac{3}{3}

\frac{1 - 0}{3}

Subtract the numbers:

1 - 0 = 1

= \frac{1}{3}

Rationalize

\frac{1}{3} : \frac{3}{3}

\frac{1}{3}

Multiply by the conjugate

\frac{3}{3}

= \frac{1 \cdot 3}{3 3}

1 \cdot 3 = 3

33 = 3

33

Apply radical rule:

a a = a

33 = 3

= 3

= \frac{3}{3}

= \frac{3}{3}

= \frac{3}{3}

arccot (π)

sin (- 3 5^{\circ})

sin (\frac{7 π}{20})

tan (arccos (- \frac{5}{6}))

0.04 π cos (π \cdot 1 - π \cdot \frac{2}{6})

What is the value of (cos(0)-sin(0))/(sqrt(3)) ?
The value of (cos(0)-sin(0))/(sqrt(3)) is (sqrt(3))/3