What is the value of 2cos(2*(3pi)/4-pi/2) ?

The value of 2cos(2*(3pi)/4-pi/2) is -2

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2cos(2*(3pi)/4-pi/2)

2 cos (2 \cdot \frac{3 π}{4} - \frac{π}{2})

- 2

Solution steps

2 cos (2 \cdot \frac{3 π}{4} - \frac{π}{2})

Simplify:

2 \cdot \frac{3 π}{4} - \frac{π}{2} = π

2 \cdot \frac{3 π}{4} - \frac{π}{2}

2 \cdot \frac{3 π}{4} = \frac{3 π}{2}

2 \cdot \frac{3 π}{4}

Multiply fractions:

a \cdot \frac{b}{c} = \frac{a \cdot b}{c}

= \frac{3 π 2}{4}

Multiply the numbers:

3 \cdot 2 = 6

= \frac{6 π}{4}

Cancel the common factor:

2

= \frac{3 π}{2}

= \frac{3 π}{2} - \frac{π}{2}

Apply rule

\frac{a}{c} \pm \frac{b}{c} = \frac{a \pm b}{c}

= \frac{3 π - π}{2}

Add similar elements:

3 π - π = 2 π

= \frac{2 π}{2}

Divide the numbers:

\frac{2}{2} = 1

= π

= 2 cos (π)

Use the following trivial identity:

cos (π) = (- 1)

cos (π)

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}

= (- 1)

= 2 (- 1)

Simplify

= - 2

20 tan (2 5^{\circ})

1 - 2 cos (\frac{5 π}{3})

arctan (\frac{- 9 - 57}{4})

arcsin (0.69282)

∣ sin (π) ∣

What is the value of 2cos(2*(3pi)/4-pi/2) ?
The value of 2cos(2*(3pi)/4-pi/2) is -2