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

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

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-2cos(-pi/4)

- 2 cos (- \frac{π}{4})

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

- 2 cos (- \frac{π}{4})

Rewrite using trig identities:

cos (- \frac{π}{4}) = \frac{2}{2}

cos (- \frac{π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{4}) = cos (\frac{π}{4})

= cos (\frac{π}{4})

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}

= \frac{2}{2}

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

Simplify

- 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

\frac{cos ( 5 0 ^{\circ} )}{cos ( 3 0 ^{\circ} )}

\frac{1 + cos ( 2 0 ^{\circ} ) - sin ( 2 0 ^{\circ} )}{1 - cos ( 2 0 ^{\circ} ) - sin ( 2 0 ^{\circ} )}

arccos (- 1) + arctan (3)

sin (3 0^{\circ}) 4

sin (3 0^{\circ}) 5