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

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

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

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

22

Decimal Notation

2.82842 \dots

Solution steps

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

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}

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}

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

Simplify

2 \cdot \frac{2}{2} + 2 \cdot \frac{2}{2} : 22

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

Add similar elements:

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

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

Multiply fractions:

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

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

Divide the numbers:

\frac{4}{2} = 2

= 22

= 22

arctan (\frac{12}{6})

arctan (\frac{12}{8})

sec (\frac{53 π}{8})

arctan (\frac{4.6}{9.2})

\frac{62}{tan ( 2 0 ^{\circ} )}

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