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

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

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-cos(-pi/4)

- cos (- \frac{π}{4})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

- 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}

= - \frac{2}{2}

2 sin (\frac{3}{5}) cos (\frac{4}{5})

arccos (\frac{11}{16})

cos (arcsin (\frac{3}{4}))

\frac{200}{cos ( 6 0 ^{\circ} )}

2 \cdot cos (\frac{π}{8}) \cdot sin (\frac{7 π}{8})