What is the value of sqrt(2)-cos(pi/2) ?

The value of sqrt(2)-cos(pi/2) is square root of 2

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sqrt(2)-cos(pi/2)

2 - cos (\frac{π}{2})

2

Decimal Notation

1.41421 \dots

Solution steps

2 - cos (\frac{π}{2})

Use the following trivial identity:

cos (\frac{π}{2}) = 0

cos (\frac{π}{2})

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}

= 0

= 2 - 0

Simplify

= 2

sec (- \frac{13 π}{4})

arccos (\frac{4}{4 2})

- 2 sec (9 0^{\circ})

arctan (1.44)

6 sin (3 5^{\circ})

What is the value of sqrt(2)-cos(pi/2) ?
The value of sqrt(2)-cos(pi/2) is square root of 2