What is the value of sqrt(3)cos(pi) ?

The value of sqrt(3)cos(pi) is -sqrt(3)

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sqrt(3)cos(pi)

3 cos (π)

- 3

Decimal Notation

- 1.73205 \dots

Solution steps

3 cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

= 3 (- 1)

Simplify

= - 3

cos (\frac{5}{13} + (- \frac{3}{5}))

tan (\frac{- 9 π}{4})

arctan (cot (13 5^{\circ}))

\frac{15}{sin ( 3 3 ^{\circ} )}

csc (16 5^{\circ})