What is the value of 2cos((3pi)/9) ?

The value of 2cos((3pi)/9) is 1

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2cos((3pi)/9)

2 cos (\frac{3 π}{9})

1

Solution steps

2 cos (\frac{3 π}{9})

Rewrite using trig identities:

cos (\frac{3 π}{9}) = \frac{1}{2}

cos (\frac{3 π}{9})

Simplify:

\frac{3 π}{9} = \frac{π}{3}

\frac{3 π}{9}

Cancel the common factor:

3

= \frac{π}{3}

= cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{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{1}{2}

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

Simplify

2 \cdot \frac{1}{2} : 1

2 \cdot \frac{1}{2}

Convert element to fraction:

2 = \frac{2}{1}

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

Cross-cancel:

2

= 1

= 1

arccos (\frac{7}{65})

cos (- 2 \cdot π)

cot (8 8^{\circ})

tan (arccos (\frac{3}{5}) + arcsin (\frac{4}{5}))

tan (7 0^{\circ}) \cdot 10