What is the value of 8cos(60)+sqrt(3)csc(60) ?

The value of 8cos(60)+sqrt(3)csc(60) is 6

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8cos(60)+sqrt(3)csc(60)

8 cos (6 0^{\circ}) + 3 csc (6 0^{\circ})

6

Solution steps

8 cos (6 0^{\circ}) + 3 csc (6 0^{\circ})

Use the following trivial identity:

cos (6 0^{\circ}) = \frac{1}{2}

cos (6 0^{\circ})

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

= 8 \cdot \frac{1}{2} + 3 \frac{2 3}{3}

Simplify

8 \cdot \frac{1}{2} + 3 \frac{2 3}{3} : 6

8 \cdot \frac{1}{2} + 3 \frac{2 3}{3}

8 \cdot \frac{1}{2} = 4

8 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 8}{2}

Multiply the numbers:

1 \cdot 8 = 8

= \frac{8}{2}

Divide the numbers:

\frac{8}{2} = 4

= 4

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

3 \frac{2 3}{3}

Multiply fractions:

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

= \frac{2 3 3}{3}

233 = 6

233

Apply radical rule:

a a = a

33 = 3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

= \frac{6}{3}

Divide the numbers:

\frac{6}{3} = 2

= 2

= 4 + 2

Add the numbers:

4 + 2 = 6

= 6

= 6

tan (\frac{3}{8})

cot (- \frac{9 π}{10})

5 sin (1 5^{\circ})

sin (\frac{25}{30})

\frac{1}{2} arctan (2)

What is the value of 8cos(60)+sqrt(3)csc(60) ?
The value of 8cos(60)+sqrt(3)csc(60) is 6