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

The value of 2*cos^2(pi/2)-sqrt(2)*sin(pi/2) is -sqrt(2)

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2cos^2(pi/2)-sqrt(2)sin(pi/2)

2 \cdot cos^{2} (\frac{π}{2}) - 2 \cdot sin (\frac{π}{2})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

2 cos^{2} (\frac{π}{2}) - 2 sin (\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

Use the following trivial identity:

sin (\frac{π}{2}) = 1

sin (\frac{π}{2})

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}

= 1

= 2 \cdot 0^{2} - 2 \cdot 1

Simplify

= - 2

tan (arcsin (\frac{- 5}{13}))

arctan (\frac{- 31}{22})

e^{2} cos (0)

arcsin (\frac{- 1}{3})

sin (12 0^{\circ}) + tan (12 0^{\circ})

What is the value of 2*cos^2(pi/2)-sqrt(2)*sin(pi/2) ?
The value of 2*cos^2(pi/2)-sqrt(2)*sin(pi/2) is -sqrt(2)