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

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

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2cos(3(pi/4))

2 cos (3 (\frac{π}{4}))

- 2

Decimal Notation

- 1.41421 \dots

Solution steps

2 cos (3 (\frac{π}{4}))

= 2 cos (3 \cdot \frac{π}{4})

Rewrite using trig identities:

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

cos (3 \cdot \frac{π}{4})

Simplify:

3 \cdot \frac{π}{4} = \frac{3 π}{4}

3 \cdot \frac{π}{4}

Multiply fractions:

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

= \frac{π 3}{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}

= - \frac{2}{2}

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

Simplify

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

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

Remove parentheses:

(- a) = - a

= - 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

11 csc (3 0^{\circ})

10 tan (3 5^{\circ})

cos (- \frac{π}{18}) \cdot sec (\frac{19 π}{18})

arctan (- \frac{5}{1})

50 cos (9 0^{\circ})