What is the value of 9cos(pi/4) ?

The value of 9cos(pi/4) is (9sqrt(2))/2

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9cos(pi/4)

9 cos (\frac{π}{4})

\frac{9 2}{2}

Decimal Notation

6.36396 \dots

Solution steps

9 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}

= 9 \cdot \frac{2}{2}

Simplify

9 \cdot \frac{2}{2} : \frac{9 2}{2}

9 \cdot \frac{2}{2}

Multiply fractions:

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

= \frac{2 \cdot 9}{2}

Apply radical rule:

2 = 2^{\frac{1}{2}}

= \frac{9 \cdot 2 ^{\frac{1}{2}}}{2}

Apply exponent rule:

\frac{x ^{a}}{x ^{b}} = \frac{1}{x ^{b - a}}

\frac{2 ^{\frac{1}{2}}}{2 ^{1}} = \frac{1}{2 ^{1 - \frac{1}{2}}}

= \frac{9}{2 ^{1 - \frac{1}{2}}}

Subtract the numbers:

1 - \frac{1}{2} = \frac{1}{2}

= \frac{9}{2 ^{\frac{1}{2}}}

Apply radical rule:

2^{\frac{1}{2}} = 2

= \frac{9}{2}

Rationalize

\frac{9}{2} : \frac{9 2}{2}

\frac{9}{2}

Multiply by the conjugate

\frac{2}{2}

= \frac{9 2}{2 2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{9 2}{2}

= \frac{9 2}{2}

= \frac{9 2}{2}

arctan (\frac{3}{- 8})

arctan (1.87)

cot (4 9^{\circ})

9.8 \cdot sin (2 0^{\circ})

sin^{2} (4 2^{\circ})