What is the value of 4cos(-pi) ?

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4cos(-pi)

4 cos (- π)

- 4

Solution steps

4 cos (- π)

Rewrite using trig identities:

cos (- π) = - 1

cos (- π)

Use the following property:

cos (- x) = cos (x)

cos (- π) = cos (π)

= 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)

= - 1

= 4 (- 1)

Simplify

= - 4

arccos (\frac{- 1}{2 5})

arctan (\frac{940.69}{983.83})

1 sin (π)

1 - 2 sin^{2} (2 0^{\circ})

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