What is the value of 6sin(pi/4)-cos(pi/4) ?

The value of 6sin(pi/4)-cos(pi/4) is 3sqrt(2)-(sqrt(2))/2

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

6sin(pi/4)-cos(pi/4)

6 sin (\frac{π}{4}) - cos (\frac{π}{4})

32 - \frac{2}{2}

Decimal Notation

3.53553 \dots

Solution steps

6 sin (\frac{π}{4}) - cos (\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}

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{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}

= 6 \cdot \frac{2}{2} - \frac{2}{2}

Simplify

6 \cdot \frac{2}{2} - \frac{2}{2} : 32 - \frac{2}{2}

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

6 \cdot \frac{2}{2} = 32

6 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 32

= 32 - \frac{2}{2}

= 32 - \frac{2}{2}

arccos (\frac{6}{145})

arccos (- \frac{2}{2}) + arctan (\frac{3}{3})

6 sin (2 (\frac{π}{2}))

sin (90. 1^{\circ})

What is the value of 6sin(pi/4)-cos(pi/4) ?
The value of 6sin(pi/4)-cos(pi/4) is 3sqrt(2)-(sqrt(2))/2