What is the value of (-cos(pi)+cos(0))(-1/2*2/3 (1)^{3/2}) ?

The value of (-cos(pi)+cos(0))(-1/2*2/3 (1)^{3/2}) is -2/3

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(-cos(pi)+cos(0))(-1/2*2/3 (1)^{3/2})

(- cos (π) + cos (0)) (- \frac{1}{2} \cdot \frac{2}{3} (1)^{\frac{3}{2}})

- \frac{2}{3}

Decimal Notation

- 0.66666 \dots

Solution steps

(- cos (π) + cos (0)) (- \frac{1}{2} \cdot \frac{2}{3} (1)^{\frac{3}{2}})

= (- cos (π) + cos (0)) (- \frac{1}{2} \cdot \frac{2}{3} \cdot 1^{\frac{3}{2}})

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)

Use the following trivial identity:

cos (0) = 1

cos (0)

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) + 1) (- \frac{1}{2} \cdot \frac{2}{3} \cdot 1^{\frac{3}{2}})

Simplify

(- (- 1) + 1) (- \frac{1}{2} \cdot \frac{2}{3} \cdot 1^{\frac{3}{2}}) : - \frac{2}{3}

(- (- 1) + 1) (- \frac{1}{2} \cdot \frac{2}{3} \cdot 1^{\frac{3}{2}})

Remove parentheses:

(- a) = - a, - (- a) = a

= - (1 + 1) \frac{1}{2} \cdot \frac{2}{3} \cdot 1^{\frac{3}{2}}

Multiply fractions:

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

= - \frac{1 \cdot 2 ( 1 + 1 ) \cdot 1 ^{\frac{3}{2}}}{2 \cdot 3}

Cancel the common factor:

2

= - \frac{1 \cdot ( 1 + 1 ) \cdot 1 ^{\frac{3}{2}}}{3}

Apply rule

1^{a} = 1

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

= - \frac{1 \cdot 1 \cdot ( 1 + 1 )}{3}

1 \cdot (1 + 1) \cdot 1 = 2

1 \cdot (1 + 1) \cdot 1

Add the numbers:

1 + 1 = 2

= 1 \cdot 2 \cdot 1

Multiply the numbers:

1 \cdot 2 \cdot 1 = 2

= 2

= - \frac{2}{3}

= - \frac{2}{3}

5 cos (2 9^{\circ})

arccos (\frac{3 π}{2})

63 cos (\frac{π}{2})

40 sin (5 3^{\circ})

arcsin (\frac{6}{14})

What is the value of (-cos(pi)+cos(0))(-1/2*2/3 (1)^{3/2}) ?
The value of (-cos(pi)+cos(0))(-1/2*2/3 (1)^{3/2}) is -2/3