What is the value of cos(-45)*cot(-150) ?

The value of cos(-45)*cot(-150) is sqrt(3/2)

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cos(-45)*cot(-150)

cos (- 4 5^{\circ}) \cdot cot (- 15 0^{\circ})

\frac{3}{2}

Decimal Notation

1.22474 \dots

Solution steps

cos (- 4 5^{\circ}) cot (- 15 0^{\circ})

Use the following property:

cot (- x) = - cot (x)

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

= cos (- 4 5^{\circ}) (- cot (15 0^{\circ}))

Use the following property:

cos (- x) = cos (x)

cos (- 4 5^{\circ}) = cos (4 5^{\circ})

= cos (4 5^{\circ}) (- cot (15 0^{\circ}))

Simplify

= - cos (4 5^{\circ}) cot (15 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:

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

= - \frac{2}{2} (- 3)

Simplify

- \frac{2}{2} (- 3) : \frac{3}{2}

- \frac{2}{2} (- 3)

Apply rule

- (- a) = a

= \frac{2}{2} 3

Multiply fractions:

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

= \frac{2 3}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

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

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

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

Subtract the numbers:

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

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

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{3}{2}

Combine same powers :

\frac{x}{y} = \frac{x}{y}

= \frac{3}{2}

= \frac{3}{2}

602 cos (4 5^{\circ})

arctan (0.0834)

tan (35 0^{\circ})

sin^{2} (1 2^{\circ})

arctan (tan (3))

What is the value of cos(-45)*cot(-150) ?
The value of cos(-45)*cot(-150) is sqrt(3/2)