What is the value of sqrt(2)cos((3pi)/4) ?

The value of sqrt(2)cos((3pi)/4) is -1

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

sqrt(2)cos((3pi)/4)

2 cos (\frac{3 π}{4})

- 1

Solution steps

2 cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 π}{4})

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}

= - \frac{2}{2}

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

Simplify

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

2 (- \frac{2}{2})

Remove parentheses:

(- a) = - a

= - 2 \frac{2}{2}

Multiply fractions:

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

= - \frac{2 2}{2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= - \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= - 1

= - 1

cos^{2} (1 8^{\circ})

3 tan (3 0^{\circ})

arcsin (sin (- \frac{5 π}{3}))

cos^{2} (6 0^{\circ}) - sin^{2} (6 0^{\circ})

cos (1 8^{\circ}) sin (- 7 2^{\circ})

What is the value of sqrt(2)cos((3pi)/4) ?
The value of sqrt(2)cos((3pi)/4) is -1