What is the value of sqrt(2)cos(-pi/4)+pi/4 ?

The value of sqrt(2)cos(-pi/4)+pi/4 is 1+pi/4

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sqrt(2)cos(-pi/4)+pi/4

2 cos (- \frac{π}{4}) + \frac{π}{4}

1 + \frac{π}{4}

Decimal Notation

1.78539 \dots

Solution steps

2 cos (- \frac{π}{4}) + \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}

= 2 \frac{2}{2} + \frac{π}{4}

Simplify

2 \frac{2}{2} + \frac{π}{4} : 1 + \frac{π}{4}

2 \frac{2}{2} + \frac{π}{4}

2 \frac{2}{2} = 1

2 \frac{2}{2}

Multiply fractions:

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

= \frac{2 2}{2}

22 = 2

22

Apply radical rule:

a a = a

22 = 2

= 2

= \frac{2}{2}

Apply rule

\frac{a}{a} = 1

= 1

= 1 + \frac{π}{4}

= 1 + \frac{π}{4}

sin (- 8 π)

sin (\frac{π}{2} + 1)

cos (\frac{3 π}{5}) cos (\frac{7 π}{30}) - sin (\frac{3 π}{5}) sin (\frac{7 π}{30})

- \frac{1}{4} csc (2 (- \frac{π}{2})^{2})

sec (\frac{π}{16})

What is the value of sqrt(2)cos(-pi/4)+pi/4 ?
The value of sqrt(2)cos(-pi/4)+pi/4 is 1+pi/4