What is the value of 7cos(pi/6) ?

The value of 7cos(pi/6) is (7sqrt(3))/2

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7cos(pi/6)

7 cos (\frac{π}{6})

\frac{7 3}{2}

Decimal Notation

6.06217 \dots

Solution steps

7 cos (\frac{π}{6})

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}

= 7 \cdot \frac{3}{2}

Simplify

7 \cdot \frac{3}{2} : \frac{7 3}{2}

7 \cdot \frac{3}{2}

Multiply fractions:

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

= \frac{3 \cdot 7}{2}

= \frac{7 3}{2}

sin^{2} (1) + cos^{2} (1)

30 sin (2 5^{\circ})

4 cos (4 5^{\circ}) - 2 sin (4 5^{\circ})

tan (\frac{7}{12})

arctan (\frac{13}{18})