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

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

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

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

\frac{2}{2} + 22

Decimal Notation

3.53553 \dots

Solution steps

cos (\frac{π}{4}) + 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}

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

Simplify

\frac{2}{2} + 4 \cdot \frac{2}{2} : \frac{2}{2} + 22

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

4 \cdot \frac{2}{2} = 22

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

= \frac{2}{2} + 22

= \frac{2}{2} + 22

\frac{12}{cos ( 2 2 ^{\circ} )}

sin (12 \cdot 0.05625) \cdot 112

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

\frac{tan ( 5 π )}{3}

arctan (- 23)

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