What is the value of 6cos(45)+3sec(180) ?

The value of 6cos(45)+3sec(180) is 3sqrt(2)-3

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6cos(45)+3sec(180)

6 cos (4 5^{\circ}) + 3 sec (18 0^{\circ})

32 - 3

Decimal Notation

1.24264 \dots

Solution steps

6 cos (4 5^{\circ}) + 3 sec (18 0^{\circ})

Use the following trivial identity:

cos (4 5^{\circ}) = \frac{2}{2}

cos (4 5^{\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{2}{2}

Use the following trivial identity:

sec (18 0^{\circ}) = (- 1)

sec (18 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}

= (- 1)

= 6 \cdot \frac{2}{2} + 3 (- 1)

Simplify

6 \cdot \frac{2}{2} + 3 (- 1) : 32 - 3

6 \cdot \frac{2}{2} + 3 (- 1)

Remove parentheses:

(- a) = - a

= 6 \cdot \frac{2}{2} - 3 \cdot 1

6 \cdot \frac{2}{2} = 32

6 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 6}{2}

Divide the numbers:

\frac{6}{2} = 3

= 32

3 \cdot 1 = 3

3 \cdot 1

Multiply the numbers:

3 \cdot 1 = 3

= 3

= 32 - 3

= 32 - 3

arctan (- \frac{3}{- 1})

csc (\frac{- π}{12})

2446.5 \cdot cos (7^{\circ})

cos (4 5^{\circ}) + sin (3 0^{\circ})

arcsin (\frac{4 3}{8})

What is the value of 6cos(45)+3sec(180) ?
The value of 6cos(45)+3sec(180) is 3sqrt(2)-3