What is the value of -2sin(60)sqrt(sec(60)) ?

The value of -2sin(60)sqrt(sec(60)) is -sqrt(6)

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-2sin(60)sqrt(sec(60))

- 2 sin (6 0^{\circ}) sec (6 0^{\circ})

- 6

Decimal Notation

- 2.44948 \dots

Solution steps

- 2 sin (6 0^{\circ}) sec (6 0^{\circ})

Use the following trivial identity:

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

sin (6 0^{\circ})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{3}{2}

Use the following trivial identity:

sec (6 0^{\circ}) = 2

sec (6 0^{\circ})

sec (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} sec (x) 1 \frac{2 3}{3} 22 Undefined - 2 - 2 - \frac{2 3}{3} 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} sec (x) - 1 - \frac{2 3}{3} - 2 - 2 Undefined 22 \frac{2 3}{3}

= 2

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

Simplify

- 2 \cdot \frac{3}{2} 2 : - 6

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

Multiply fractions:

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

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

Cancel the common factor:

2

= - 32

Apply radical rule:

a b = a \cdot b

32 = 3 \cdot 2

= - 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 6

= - 6

= - 6

3 cos (30 0^{\circ})

\frac{sin ( 8 0 ^{\circ} )}{7}

arccos (- \frac{1}{7})

\frac{sin ( 1 0 ^{\circ} )}{sin ( 6 )}

cos (93.30 9^{\circ})

What is the value of -2sin(60)sqrt(sec(60)) ?
The value of -2sin(60)sqrt(sec(60)) is -sqrt(6)