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

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

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sqrt(2)cos(-pi/2)+pi/2

2 cos (- \frac{π}{2}) + \frac{π}{2}

\frac{π}{2}

Decimal

1.57079 \dots

Solution steps

2 cos (- \frac{π}{2}) + \frac{π}{2}

Rewrite using trig identities:

cos (- \frac{π}{2}) = 0

cos (- \frac{π}{2})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{2}) = cos (\frac{π}{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

= 0

= 2 \cdot 0 + \frac{π}{2}

Simplify

= \frac{π}{2}

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