What is the value of 7cos((3pi)/4)-7cos(pi/4) ?

The value of 7cos((3pi)/4)-7cos(pi/4) is -7sqrt(2)

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7cos((3pi)/4)-7cos(pi/4)

7 cos (\frac{3 π}{4}) - 7 cos (\frac{π}{4})

- 72

Decimal Notation

- 9.89949 \dots

Solution steps

7 cos (\frac{3 π}{4}) - 7 cos (\frac{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}

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}

= 7 (- \frac{2}{2}) - 7 \cdot \frac{2}{2}

Simplify

7 (- \frac{2}{2}) - 7 \cdot \frac{2}{2} : - 72

7 (- \frac{2}{2}) - 7 \cdot \frac{2}{2}

Remove parentheses:

(- a) = - a

= - 7 \cdot \frac{2}{2} - 7 \cdot \frac{2}{2}

Add similar elements:

- 7 \cdot \frac{2}{2} - 7 \cdot \frac{2}{2} = - 14 \cdot \frac{2}{2}

= - 14 \cdot \frac{2}{2}

Multiply fractions:

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

= - \frac{2 \cdot 14}{2}

Divide the numbers:

\frac{14}{2} = 7

= - 72

= - 72

\frac{( 7.01 ) ^{2} \cdot sin ( 2 \cdot 35 )}{15.39}

tan (arccsc (- 5))

10 cos (2 π)

58 cos (54.0 4^{\circ})

tan (- \frac{5}{12})

What is the value of 7cos((3pi)/4)-7cos(pi/4) ?
The value of 7cos((3pi)/4)-7cos(pi/4) is -7sqrt(2)