What is the value of (2csc(60))^2 ?

The value of (2csc(60))^2 is 16/3

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(2csc(60))^2

(2 csc (6 0^{\circ}))^{2}

\frac{16}{3}

Decimal Notation

5.33333 \dots

Solution steps

(2 csc (6 0^{\circ}))^{2}

Use the following trivial identity:

csc (6 0^{\circ}) = \frac{2 3}{3}

csc (6 0^{\circ})

csc (x)

periodicity table with

36 0^{\circ} n

cycle:

x 0 3 0^{\circ} 4 5^{\circ} 6 0^{\circ} 9 0^{\circ} 12 0^{\circ} 13 5^{\circ} 15 0^{\circ} csc (x) Undefiend 22 \frac{2 3}{3} 1 \frac{2 3}{3} 22 x 18 0^{\circ} 21 0^{\circ} 22 5^{\circ} 24 0^{\circ} 27 0^{\circ} 30 0^{\circ} 31 5^{\circ} 33 0^{\circ} csc (x) Undefiend - 2 - 2 - \frac{2 3}{3} - 1 - \frac{2 3}{3} - 2 - 2

= \frac{2 3}{3}

= (2 \cdot \frac{2 3}{3})^{2}

Simplify

(2 \cdot \frac{2 3}{3})^{2} : \frac{16}{3}

(2 \cdot \frac{2 3}{3})^{2}

Multiply

2 \cdot \frac{2 3}{3} : \frac{4}{3}

2 \cdot \frac{2 3}{3}

Multiply fractions:

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

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

Multiply the numbers:

2 \cdot 2 = 4

= \frac{4 3}{3}

Apply radical rule:

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

= \frac{4 \cdot 3 ^{\frac{1}{2}}}{3}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

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

= \frac{4}{3 ^{1 - \frac{1}{2}}}

Subtract the numbers:

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

= \frac{4}{3 ^{\frac{1}{2}}}

Apply radical rule:

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

= \frac{4}{3}

= (\frac{4}{3})^{2}

Apply exponent rule:

(\frac{a}{b})^{c} = \frac{a ^{c}}{b ^{c}}

= \frac{4 ^{2}}{( 3 ) ^{2}}

(3)^{2} : 3

Apply radical rule:

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

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

Apply exponent rule:

(a^{b})^{c} = a^{b c}

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

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

\frac{1}{2} \cdot 2

Multiply fractions:

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

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

Cancel the common factor:

2

= 1

= 3

= \frac{4 ^{2}}{3}

4^{2} = 16

= \frac{16}{3}

= \frac{16}{3}

sin (2) (\frac{3 π}{2})

\frac{sin ( 7 5 ^{\circ} ) - sin ( 1 5 ^{\circ} )}{cos ( 7 5 ^{\circ} ) + cos ( 1 5 ^{\circ} )}

(sin (3))^{2}

3 tan (6 5^{\circ})

- 4 cos (- 4)