What is the value of 2cos(pi/4)-1 ?

The value of 2cos(pi/4)-1 is sqrt(2)-1

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2cos(pi/4)-1

2 cos (\frac{π}{4}) - 1

2 - 1

Decimal Notation

0.41421 \dots

Solution steps

2 cos (\frac{π}{4}) - 1

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}

= 2 \cdot \frac{2}{2} - 1

Simplify

2 \cdot \frac{2}{2} - 1 : 2 - 1

2 \cdot \frac{2}{2} - 1

2 \cdot \frac{2}{2} = 2

2 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 2}{2}

Cancel the common factor:

2

= 2

= 2 - 1

= 2 - 1

60 sin (5 0^{\circ})

- 4 sin (4)

cos (\frac{11}{6} π)

arcsin (\frac{2.1}{4})

cos^{2} (1) - sin^{2} (1)