What is the value of 5+4cos(-pi/4) ?

The value of 5+4cos(-pi/4) is 5+2sqrt(2)

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5+4cos(-pi/4)

5 + 4 cos (- \frac{π}{4})

5 + 22

Decimal Notation

7.82842 \dots

Solution steps

5 + 4 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}

= 5 + 4 \cdot \frac{2}{2}

Simplify

5 + 4 \cdot \frac{2}{2} : 5 + 22

5 + 4 \cdot \frac{2}{2}

4 \cdot \frac{2}{2} = 22

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

= 5 + 22

= 5 + 22

cos (arcsin (\frac{5}{13}) + arctan (\frac{7}{24}))

cot (\frac{3 π}{11})

cos (2 arccos (1))

sin (\frac{11 π}{6}) + cos (\frac{5 π}{3})

2 cos (\frac{π}{2}) - (\frac{π}{2})