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

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

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2(cos(pi/4)+sin(pi/4))

2 (cos (\frac{π}{4}) + sin (\frac{π}{4}))

22

Decimal Notation

2.82842 \dots

Solution steps

2 (cos (\frac{π}{4}) + sin (\frac{π}{4}))

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

cos (\frac{π}{4})

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{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{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}

= 2 (\frac{2}{2} + \frac{2}{2})

Simplify

2 (\frac{2}{2} + \frac{2}{2}) : 22

2 (\frac{2}{2} + \frac{2}{2})

Simplify

\frac{2}{2} + \frac{2}{2} : 2

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

Apply rule

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

= \frac{2 + 2}{2}

Add similar elements:

2 + 2 = 22

= \frac{2 2}{2}

Divide the numbers:

\frac{2}{2} = 1

= 2

= 22

= 22

arcsin (\frac{65}{1646.86})

9.02 cos (30.8 3^{\circ})

e^{c o s (2 π)}

\frac{30}{sin ( 6 0 ^{\circ} )}

cos (\frac{4}{3.3 8 ^{2} + 4 ^{2}})

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