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

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

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-4cos((3pi)/4)

- 4 cos (\frac{3 π}{4})

22

Decimal Notation

2.82842 \dots

Solution steps

- 4 cos (\frac{3 π}{4})

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

cos (\frac{3 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}

= - 4 (- \frac{2}{2})

Simplify

- 4 (- \frac{2}{2}) : 22

- 4 (- \frac{2}{2})

Apply rule

- (- a) = a

= 4 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 4}{2}

Divide the numbers:

\frac{4}{2} = 2

= 22

= 22

tan (\frac{π}{4}) - tan (0)

arcsin (7)

arccosh (2)

\frac{sin ( \frac{π}{2} )}{\frac{π}{2}}

arccos (cos (2 π))