What is the value of 3e^0cos(pi/3) ?

The value of 3e^0cos(pi/3) is 3/2

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3e^0cos(pi/3)

3 e^{0} cos (\frac{π}{3})

\frac{3}{2}

Decimal Notation

1.5

Solution steps

3 e^{0} cos (\frac{π}{3})

Use the following trivial identity:

cos (\frac{π}{3}) = \frac{1}{2}

cos (\frac{π}{3})

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{1}{2}

= 3 e^{0} \frac{1}{2}

Simplify

3 e^{0} \frac{1}{2} : \frac{3}{2}

3 e^{0} \frac{1}{2}

Apply rule

a^{0} = 1, a \neq = 0

e^{0} = 1

= 3 \cdot 1 \cdot \frac{1}{2}

Multiply fractions:

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

= 1 \cdot \frac{1 \cdot 3}{2}

Multiply the numbers:

1 \cdot 3 = 3

= 1 \cdot \frac{3}{2}

Multiply:

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

= \frac{3}{2}

= \frac{3}{2}

csc (\frac{- 3 π}{4})

sin (\frac{π}{2} + \frac{π}{6})

cos (2 arcsin (\frac{9}{41}))

sin (\frac{24}{25})

sin (\frac{3}{5} + \frac{5}{13})