What is the value of sin(pi/2+pi/4) ?

The value of sin(pi/2+pi/4) is (sqrt(2))/2

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sin(pi/2+pi/4)

sin (\frac{π}{2} + \frac{π}{4})

\frac{2}{2}

Decimal Notation

0.70710 \dots

Solution steps

sin (\frac{π}{2} + \frac{π}{4})

Simplify:

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

\frac{π}{2} + \frac{π}{4}

Least Common Multiplier of

2, 4 : 4

2, 4

Least Common Multiplier (LCM)

Prime factorization of

2 : 2

2

2

is a prime number, therefore no factorization is possible

= 2

Prime factorization of

4 : 2 \cdot 2

4

4

divides by

24 = 2 \cdot 2

= 2 \cdot 2

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

2

4

= 2 \cdot 2

Multiply the numbers:

2 \cdot 2 = 4

= 4

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

4

For

\frac{π}{2} :

multiply the denominator and numerator by

2

\frac{π}{2} = \frac{π 2}{2 \cdot 2} = \frac{π 2}{4}

= \frac{π 2}{4} + \frac{π}{4}

Since the denominators are equal, combine the fractions:

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

= \frac{π 2 + π}{4}

Add similar elements:

2 π + π = 3 π

= \frac{3 π}{4}

= sin (\frac{3 π}{4})

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

sin (\frac{3 π}{4})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

= \frac{2}{2}

- 4 cos (\frac{2 π}{3})

sin (\frac{7}{2} π)

cos (2 arccos (\frac{1}{3}))

3 sin (3 7^{\circ})

arcsin (cos (\frac{3 π}{5}))

What is the value of sin(pi/2+pi/4) ?
The value of sin(pi/2+pi/4) is (sqrt(2))/2