What is the value of cos(150)+sin(45)+1/2 cot(-330) ?

The value of cos(150)+sin(45)+1/2 cot(-330) is (sqrt(2))/2

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cos(150)+sin(45)+1/2 cot(-330)

Solution

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

Solution

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

cos (15 0^{\circ}) + sin (4 5^{\circ}) + \frac{1}{2} cot (- 33 0^{\circ})

Use the following trivial identity:

cos (15 0^{\circ}) = - \frac{3}{2}

cos (15 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{3}{2}

Use the following trivial identity:

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

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

Rewrite using trig identities:

cot (- 33 0^{\circ}) = 3

cot (- 33 0^{\circ})

Use the following property:

cot (- x) = - cot (x)

cot (- 33 0^{\circ}) = - cot (33 0^{\circ})

= - cot (33 0^{\circ})

cot (33 0^{\circ}) = cot (15 0^{\circ})

cot (33 0^{\circ})

Rewrite

33 0^{\circ}

18 0^{\circ} + 15 0^{\circ}

= cot (18 0^{\circ} + 15 0^{\circ})

Apply the periodicity of

cot

cot (x + 18 0^{\circ}) = cot (x)

cot (18 0^{\circ} + 15 0^{\circ}) = cot (15 0^{\circ})

= cot (15 0^{\circ})

= - cot (15 0^{\circ})

Use the following trivial identity:

cot (15 0^{\circ}) = - 3

cot (15 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

= - (- 3)

Simplify

= 3

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

Simplify

- \frac{3}{2} + \frac{2}{2} + \frac{1}{2} 3 : \frac{2}{2}

- \frac{3}{2} + \frac{2}{2} + \frac{1}{2} 3

Combine the fractions

- \frac{3}{2} + \frac{2}{2} : \frac{- 3 + 2}{2}

Apply rule

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

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

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

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

\frac{1}{2} 3

Multiply fractions:

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

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

Multiply:

1 \cdot 3 = 3

= \frac{3}{2}

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

Apply rule

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

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

Add similar elements:

- 3 + 3 = 0

= \frac{2}{2}

= \frac{2}{2}

Popular Examples

arctan((8sqrt(3))/(-8))

arctan (\frac{8 3}{- 8})

-e^0cos(0)

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cos(6*pi)

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cos(155)cos(20)+sin(155)sin(20)

cos (15 5^{\circ}) cos (2 0^{\circ}) + sin (15 5^{\circ}) sin (2 0^{\circ})

sin(3)(pi/2)

sin (3) (\frac{π}{2})

Frequently Asked Questions (FAQ)

What is the value of cos(150)+sin(45)+1/2 cot(-330) ?
The value of cos(150)+sin(45)+1/2 cot(-330) is (sqrt(2))/2