What is the value of -2cos((2pi)/3)csc(((pi/3))/2) ?

The value of -2cos((2pi)/3)csc(((pi/3))/2) is 2

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-2cos((2pi)/3)csc(((pi/3))/2)

- 2 cos (\frac{2 π}{3}) csc (\frac{( \frac{π}{3} )}{2})

2

Solution steps

- 2 cos (\frac{2 π}{3}) csc (\frac{( \frac{π}{3} )}{2})

= - 2 cos (\frac{2 π}{3}) csc (\frac{\frac{π}{3}}{2})

Simplify:

\frac{\frac{π}{3}}{2} = \frac{π}{6}

\frac{\frac{π}{3}}{2}

Apply the fraction rule:

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

= \frac{π}{3 \cdot 2}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{π}{6}

= - 2 cos (\frac{2 π}{3}) csc (\frac{π}{6})

Use the following trivial identity:

cos (\frac{2 π}{3}) = - \frac{1}{2}

cos (\frac{2 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}

Use the following trivial identity:

csc (\frac{π}{6}) = 2

csc (\frac{π}{6})

csc (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} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 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} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= 2

= - 2 (- \frac{1}{2}) \cdot 2

Simplify

- 2 (- \frac{1}{2}) \cdot 2 : 2

- 2 (- \frac{1}{2}) \cdot 2

Apply rule

- (- a) = a

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

Multiply fractions:

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

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

Cancel the common factor:

2

= 1 \cdot 2

Multiply the numbers:

1 \cdot 2 = 2

= 2

= 2

\frac{1}{2} (7) (10) (cos (\frac{π}{4})) (- \frac{π}{45})

3 \cdot cot (\frac{45}{2}) \cdot cot (\frac{75}{2}) \cdot cot (\frac{60}{2})

\frac{sin ( 30 0 ^{\circ} ) + cos ( 15 0 ^{\circ} )}{tan ( 12 0 ^{\circ} ) + cot ( 24 0 ^{\circ} )}

sin (\frac{π}{4}) cos (\frac{π}{3}) - cos (\frac{π}{4}) sin (\frac{π}{3})

4983 \cdot cos (4 0^{\circ})

What is the value of -2cos((2pi)/3)csc(((pi/3))/2) ?
The value of -2cos((2pi)/3)csc(((pi/3))/2) is 2