What is the value of cos(pi/2+pi/3) ?

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

English

Español

Português

Français

Deutsch

Italiano

Русский

中文(简体)

한국어

日本語

Tiếng Việt

עברית

العربية

Popular >

cos(pi/2+pi/3)

Solution

cos (\frac{π}{2} + \frac{π}{3})

Solution

- \frac{3}{2}

Decimal Notation

- 0.86602 \dots

Solution steps

cos (\frac{π}{2} + \frac{π}{3})

Simplify:

\frac{π}{2} + \frac{π}{3} = \frac{5 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 = 5 π

= \frac{5 π}{6}

= cos (\frac{5 π}{6})

Use the following trivial identity:

cos (\frac{5 π}{6}) = - \frac{3}{2}

cos (\frac{5 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}

= - \frac{3}{2}

Popular Examples

arccos(sqrt(1/3))

arccos (\frac{1}{3})

arctan(sqrt((tan(9))^2+(tan(1))^2))

arctan ((tan (9^{\circ}))^{2} + (tan (1^{\circ}))^{2})

1-cos(60)-2sin^2(30)

1 - cos (6 0^{\circ}) - 2 sin^{2} (3 0^{\circ})

600*sin(60)

600 \cdot sin (6 0^{\circ})

(sin(pi/8)+cos(pi/8))^2

(sin (\frac{π}{8}) + cos (\frac{π}{8}))^{2}

Frequently Asked Questions (FAQ)

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