What is the value of -3cos(-pi/6)-4tan(-pi/6) ?

The value of -3cos(-pi/6)-4tan(-pi/6) is -(sqrt(3))/6

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Popular Trigonometry >

-3cos(-pi/6)-4tan(-pi/6)

Solution

- 3 cos (- \frac{π}{6}) - 4 tan (- \frac{π}{6})

Solution

- \frac{3}{6}

Decimal

- 0.28867 \dots

Solution steps

- 3 cos (- \frac{π}{6}) - 4 tan (- \frac{π}{6})

Use the following property:

tan (- x) = - tan (x)

tan (- \frac{π}{6}) = - tan (\frac{π}{6})

= - 3 cos (- \frac{π}{6}) - 4 (- tan (\frac{π}{6}))

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{6}) = cos (\frac{π}{6})

= - 3 cos (\frac{π}{6}) - 4 (- tan (\frac{π}{6}))

Simplify

= - 3 cos (\frac{π}{6}) + 4 tan (\frac{π}{6})

Use the following trivial identity:

cos (\frac{π}{6}) = \frac{3}{2}

cos (\frac{π}{6})

cos (x)

periodicity table with

2 πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} cos (x) 1 \frac{3}{2} \frac{2}{2} \frac{1}{2} 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} x π \frac{7 π}{6} \frac{5 π}{4} \frac{4 π}{3} \frac{3 π}{2} \frac{5 π}{3} \frac{7 π}{4} \frac{11 π}{6} 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:

tan (\frac{π}{6}) = \frac{3}{3}

tan (\frac{π}{6})

tan (x)

periodicity table with

πn

cycle:

x 0 \frac{π}{6} \frac{π}{4} \frac{π}{3} \frac{π}{2} \frac{2 π}{3} \frac{3 π}{4} \frac{5 π}{6} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

= - 3 \cdot \frac{3}{2} + 4 \cdot \frac{3}{3}

Simplify

- 3 \cdot \frac{3}{2} + 4 \cdot \frac{3}{3} : - \frac{3}{6}

- 3 \cdot \frac{3}{2} + 4 \cdot \frac{3}{3}

Multiply

3 \cdot \frac{3}{2} : \frac{3 3}{2}

3 \cdot \frac{3}{2}

Multiply fractions:

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

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

= - \frac{3 3}{2} + 4 \cdot \frac{3}{3}

Multiply

4 \cdot \frac{3}{3} : \frac{4 3}{3}

4 \cdot \frac{3}{3}

Multiply fractions:

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

= \frac{3 \cdot 4}{3}

= - \frac{3 3}{2} + \frac{4 3}{3}

Least Common Multiplier of

2, 3 : 6

2, 3

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Multiply each factor the greatest number of times it occurs in either

2

3

= 2 \cdot 3

Multiply the numbers:

2 \cdot 3 = 6

= 6

Adjust Fractions based on the LCM

Multiply each numerator by the same amount needed to multiply its

corresponding denominator to turn it into the LCM

6

For

\frac{3 \cdot 3}{2} :

multiply the denominator and numerator by

3

\frac{3 \cdot 3}{2} = \frac{3 \cdot 3 \cdot 3}{2 \cdot 3} = \frac{9 3}{6}

For

\frac{3 \cdot 4}{3} :

multiply the denominator and numerator by

2

\frac{3 \cdot 4}{3} = \frac{3 \cdot 4 \cdot 2}{3 \cdot 2} = \frac{8 3}{6}

= - \frac{9 3}{6} + \frac{8 3}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{- 9 3 + 8 3}{6}

Add similar elements:

- 93 + 83 = - 3

= \frac{- 3}{6}

Apply the fraction rule:

\frac{- a}{b} = - \frac{a}{b}

= - \frac{3}{6}

= - \frac{3}{6}

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Frequently Asked Questions (FAQ)

What is the value of -3cos(-pi/6)-4tan(-pi/6) ?
The value of -3cos(-pi/6)-4tan(-pi/6) is -(sqrt(3))/6