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

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

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

(cos (\frac{π}{4}) + 2)^{4}

(\frac{2}{2} + 2)^{4}

Decimal Notation

53.70584 \dots

Solution steps

(cos (\frac{π}{4}) + 2)^{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}

= (\frac{2}{2} + 2)^{4}

arccos (0.78155)

(π - cos (π)) - (0 - cos (0))

sin^{2} (5 0^{\circ}) + sin^{2} (4 0^{\circ})

csc (72 0^{\circ})

- sin (0) sin (π)

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