What is the value of cos(pi/6)+tan(pi/3)+3csc(pi/4)-6tan(pi/4) ?

The value of cos(pi/6)+tan(pi/3)+3csc(pi/4)-6tan(pi/4) is (sqrt(3))/2+sqrt(3)+3sqrt(2)-6

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cos(pi/6)+tan(pi/3)+3csc(pi/4)-6tan(pi/4)

cos (\frac{π}{6}) + tan (\frac{π}{3}) + 3 csc (\frac{π}{4}) - 6 tan (\frac{π}{4})

\frac{3}{2} + 3 + 32 - 6

Decimal Notation

0.84071 \dots

Solution steps

cos (\frac{π}{6}) + tan (\frac{π}{3}) + 3 csc (\frac{π}{4}) - 6 tan (\frac{π}{4})

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}

Use the following trivial identity:

tan (\frac{π}{3}) = 3

tan (\frac{π}{3})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 3

Use the following trivial identity:

csc (\frac{π}{4}) = 2

csc (\frac{π}{4})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

Use the following trivial identity:

tan (\frac{π}{4}) = 1

tan (\frac{π}{4})

tan (x)

periodicity table with

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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= 1

= \frac{3}{2} + 3 + 32 - 6 \cdot 1

Simplify

= \frac{3}{2} + 3 + 32 - 6

\frac{cos ( \frac{π}{2} ) - cos ( \frac{4 π}{3} )}{2 sin ( \frac{5 π}{6} )}

35 sin (1 0^{\circ}) - (9.8 \cdot 7.5)

arcsin (\frac{3}{18})

cot (12 7^{\circ})

arcsin (0.69264)

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