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

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

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

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

- 2

Solution steps

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

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

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}

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

Simplify

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

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

Convert element to fraction:

2 = \frac{2}{1}

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

Convert element to fraction:

2 = \frac{2}{1}

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

Multiply fractions:

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

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

Cancel the common factor:

2

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

Cancel the common factor:

1

= - \frac{2}{1}

Apply rule

\frac{a}{1} = a

= - 2

= - 2

\frac{1}{sin ( \frac{- 3 π}{4} )}

tan (\frac{11}{60})

\frac{π}{2} cos (π)

e - 4 π + sin (1)

csc^{2} (9 0^{\circ})

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