What is the value of cos((13pi)/6)-tan((8pi)/3) ?

The value of cos((13pi)/6)-tan((8pi)/3) is (sqrt(3))/2+sqrt(3)

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos((13pi)/6)-tan((8pi)/3)

Solution

cos (\frac{13 π}{6}) - tan (\frac{8 π}{3})

Solution

\frac{3}{2} + 3

Decimal Notation

2.59807 \dots

Solution steps

cos (\frac{13 π}{6}) - tan (\frac{8 π}{3})

cos (\frac{13 π}{6}) = cos (\frac{π}{6})

cos (\frac{13 π}{6})

Rewrite

\frac{13 π}{6}

2 π + \frac{π}{6}

= cos (2 π + \frac{π}{6})

Apply the periodicity of

cos

cos (x + 2 π) = cos (x)

cos (2 π + \frac{π}{6}) = cos (\frac{π}{6})

= cos (\frac{π}{6})

= cos (\frac{π}{6}) - tan (\frac{8 π}{3})

tan (\frac{8 π}{3}) = tan (\frac{2 π}{3})

tan (\frac{8 π}{3})

Rewrite

\frac{8 π}{3}

π \cdot 2 + \frac{2 π}{3}

= tan (π 2 + \frac{2 π}{3})

Apply the periodicity of

tan

tan (x + π \cdot k) = tan (x)

tan (π \cdot 2 + \frac{2 π}{3}) = tan (\frac{2 π}{3})

= tan (\frac{2 π}{3})

= cos (\frac{π}{6}) - tan (\frac{2 π}{3})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

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{3}{2}

Rewrite using trig identities:

tan (\frac{2 π}{3}) = - 3

tan (\frac{2 π}{3})

Rewrite using trig identities:

\frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

tan (\frac{2 π}{3})

Use the basic trigonometric identity:

tan (x) = \frac{sin ( x )}{cos ( x )}

= \frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

= \frac{sin ( \frac{2 π}{3} )}{cos ( \frac{2 π}{3} )}

Use the following trivial identity:

sin (\frac{2 π}{3}) = \frac{3}{2}

sin (\frac{2 π}{3})

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{3}{2}

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 π}{3})

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{1}{2}

= \frac{\frac{3}{2}}{- \frac{1}{2}}

Simplify

\frac{\frac{3}{2}}{- \frac{1}{2}} : - 3

\frac{\frac{3}{2}}{- \frac{1}{2}}

Apply the fraction rule:

\frac{a}{- b} = - \frac{a}{b}

= - \frac{\frac{3}{2}}{\frac{1}{2}}

Divide fractions:

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

= - \frac{3 \cdot 2}{2 \cdot 1}

Refine

= - \frac{3 \cdot 2}{2}

Cancel the common factor:

2

= - 3

= - 3

= \frac{3}{2} - (- 3)

Simplify

= \frac{3}{2} + 3

Popular Examples

500*sin(45)

500 \cdot sin (4 5^{\circ})

cos^6(1)

cos^{6} (1)

(1)(1-20/100+1/(2pi)(sin(2pi)(20/100)))

(1) (1 - \frac{20}{100} + \frac{1}{2 π} (sin (2 π) (\frac{20}{100})))

csc(30)-tan(45)

csc (3 0^{\circ}) - tan (4 5^{\circ})

sin(2pi-1pi)

sin (2 π - 1 π)

Frequently Asked Questions (FAQ)

What is the value of cos((13pi)/6)-tan((8pi)/3) ?
The value of cos((13pi)/6)-tan((8pi)/3) is (sqrt(3))/2+sqrt(3)