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

The value of cos(3(pi/3)) is -1

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cos(3(pi/3))

cos (3 (\frac{π}{3}))

- 1

Solution steps

cos (3 (\frac{π}{3}))

= cos (3 \cdot \frac{π}{3})

Simplify:

3 \cdot \frac{π}{3} = π

3 \cdot \frac{π}{3}

Multiply fractions:

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

= \frac{π 3}{3}

Cancel the common factor:

3

= 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

sec (\frac{π}{4}) + tan (\frac{π}{4})

sin (arccos (\frac{1}{3}))

arctan (1.53)

sin^{3} (27 0^{\circ}) + csc^{2} (49 5^{\circ})

cos (53. 1^{\circ})