What is the value of 2-2sin(pi/4) ?

The value of 2-2sin(pi/4) is 2-sqrt(2)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

2-2sin(pi/4)

2 - 2 sin (\frac{π}{4})

2 - 2

Decimal Notation

0.58578 \dots

Solution steps

2 - 2 sin (\frac{π}{4})

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

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}

= \frac{2}{2}

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

Simplify

2 - 2 \cdot \frac{2}{2} : 2 - 2

2 - 2 \cdot \frac{2}{2}

2 \cdot \frac{2}{2} = 2

2 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 2}{2}

Cancel the common factor:

2

= 2

= 2 - 2

= 2 - 2

\frac{sin ( 3 5 ^{\circ} )}{1.33}

- 3 cos^{2} (π)

34 sin (3 0^{\circ})

sec (0.58)

tan (\frac{π}{4}) sec (\frac{π}{4})