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

Solution steps

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

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (\frac{π}{4}) = \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} + 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)