What is the value of (14cos(60)+sqrt(3)cot(30))/(2sec(60)) ?

The value of (14cos(60)+sqrt(3)cot(30))/(2sec(60)) is 5/2

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(14cos(60)+sqrt(3)cot(30))/(2sec(60))

\frac{14 cos ( 6 0 ^{\circ} ) + 3 cot ( 3 0 ^{\circ} )}{2 sec ( 6 0 ^{\circ} )}

\frac{5}{2}

Decimal Notation

2.5

Solution steps

\frac{14 cos ( 6 0 ^{\circ} ) + 3 cot ( 3 0 ^{\circ} )}{2 sec ( 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:

cot (3 0^{\circ}) = 3

cot (3 0^{\circ})

cot (x)

periodicity table with

18 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} cot (x) \mp \infty 31 \frac{3}{3} 0 - \frac{3}{3} - 1 - 3

= 3

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

= \frac{14 \cdot \frac{1}{2} + 3 3}{2 \cdot 2}

Simplify

\frac{14 \cdot \frac{1}{2} + 3 3}{2 \cdot 2} : \frac{5}{2}

\frac{14 \cdot \frac{1}{2} + 3 3}{2 \cdot 2}

14 \cdot \frac{1}{2} + 33 = 14 \cdot \frac{1}{2} + 3

14 \cdot \frac{1}{2} + 33

Apply radical rule:

a a = a

33 = 3

= 14 \cdot \frac{1}{2} + 3

= \frac{14 \cdot \frac{1}{2} + 3}{2 \cdot 2}

Multiply the numbers:

2 \cdot 2 = 4

= \frac{14 \cdot \frac{1}{2} + 3}{4}

14 \cdot \frac{1}{2} = 7

14 \cdot \frac{1}{2}

Multiply fractions:

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

= \frac{1 \cdot 14}{2}

Multiply the numbers:

1 \cdot 14 = 14

= \frac{14}{2}

Divide the numbers:

\frac{14}{2} = 7

= 7

= \frac{7 + 3}{4}

Add the numbers:

7 + 3 = 10

= \frac{10}{4}

Cancel the common factor:

2

= \frac{5}{2}

= \frac{5}{2}

sin (5 8^{\circ}) - cos (3 2^{\circ})

arctan (\frac{6.81}{9.8} + 0.5)

cos (36 π)

4 (cos (π) + i sin (π))

5 sin (\frac{2 π}{3}) + cos (\frac{2 π}{3})

What is the value of (14cos(60)+sqrt(3)cot(30))/(2sec(60)) ?
The value of (14cos(60)+sqrt(3)cot(30))/(2sec(60)) is 5/2