What is the value of tan(30)+cos(30) ?

The value of tan(30)+cos(30) is (5sqrt(3))/6

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tan(30)+cos(30)

Solution

tan (3 0^{\circ}) + cos (3 0^{\circ})

Solution

\frac{5 3}{6}

Decimal Notation

1.44337 \dots

Solution steps

tan (3 0^{\circ}) + cos (3 0^{\circ})

Use the following trivial identity:

tan (3 0^{\circ}) = \frac{3}{3}

tan (3 0^{\circ})

tan (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} tan (x) 0 \frac{3}{3} 13 \pm \infty - 3 - 1 - \frac{3}{3}

= \frac{3}{3}

Use the following trivial identity:

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

cos (3 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}

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

Simplify

\frac{3}{3} + \frac{3}{2} : \frac{5 3}{6}

\frac{3}{3} + \frac{3}{2}

Least Common Multiplier of

3, 2 : 6

3, 2

Least Common Multiplier (LCM)

Prime factorization of

3 : 3

3

3

is a prime number, therefore no factorization is possible

= 3

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

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

3

2

= 3 \cdot 2

Multiply the numbers:

3 \cdot 2 = 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}{3} :

multiply the denominator and numerator by

2

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

For

\frac{3}{2} :

multiply the denominator and numerator by

3

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

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

Since the denominators are equal, combine the fractions:

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

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

Add similar elements:

23 + 33 = 53

= \frac{5 3}{6}

= \frac{5 3}{6}

Popular Examples

cos(pi/6)-sin(pi/6)

cos (\frac{π}{6}) - sin (\frac{π}{6})

sin(380)

sin (38 0^{\circ})

arccos(43/48)

arccos (\frac{43}{48})

(132)/(tan(5))

\frac{132}{tan ( 5 )}

tan(-1020)

tan (- 102 0^{\circ})

Frequently Asked Questions (FAQ)

What is the value of tan(30)+cos(30) ?
The value of tan(30)+cos(30) is (5sqrt(3))/6