What is the value of tan(pi/2-pi/3) ?

The value of tan(pi/2-pi/3) is (sqrt(3))/3

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tan(pi/2-pi/3)

Solution

tan (\frac{π}{2} - \frac{π}{3})

Solution

\frac{3}{3}

Decimal Notation

0.57735 \dots

Solution steps

tan (\frac{π}{2} - \frac{π}{3})

Simplify:

\frac{π}{2} - \frac{π}{3} = \frac{π}{6}

\frac{π}{2} - \frac{π}{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{π}{2} :

multiply the denominator and numerator by

3

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

For

\frac{π}{3} :

multiply the denominator and numerator by

2

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

= \frac{π 3}{6} - \frac{π 2}{6}

Since the denominators are equal, combine the fractions:

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

= \frac{π 3 - π 2}{6}

Add similar elements:

3 π - 2 π = π

= \frac{π}{6}

= tan (\frac{π}{6})

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}

= \frac{3}{3}

Popular Examples

sin(pi/2+(ln(2+sqrt(3)))/i)

sin (\frac{π}{2} + \frac{ln ( 2 + 3 )}{i})

15sin(20)

15 sin (2 0^{\circ})

22sin(45)

22 sin (4 5^{\circ})

sec(pi/4)*tan(pi/4)

sec (\frac{π}{4}) \cdot tan (\frac{π}{4})

sin(11.5)

sin (11. 5^{\circ})

Frequently Asked Questions (FAQ)

What is the value of tan(pi/2-pi/3) ?
The value of tan(pi/2-pi/3) is (sqrt(3))/3