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Popular >

cos(3 pi/3)

Solution

cos (3 \frac{π}{3})

Solution

- 1

Solution steps

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

Popular Examples

(sin(2)(-1.5))/(-1.5)

\frac{sin ( 2 ) ( - 1.5 )}{- 1.5}

-cot(pi/6)csc(pi/6)

- cot (\frac{π}{6}) csc (\frac{π}{6})

tan(arctan(4/3)-arctan(1/7))

tan (arctan (\frac{4}{3}) - arctan (\frac{1}{7}))

1/2 sin(2(pi/2))

\frac{1}{2} sin (2 (\frac{π}{2}))

arcsin((1.5)/(2.6))

arcsin (\frac{1.5}{2.6})

Frequently Asked Questions (FAQ)

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