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

The value of cos(-pi/4)+sin(-pi/4) is 0

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cos(-pi/4)+sin(-pi/4)

cos (- \frac{π}{4}) + sin (- \frac{π}{4})

0

Solution steps

cos (- \frac{π}{4}) + sin (- \frac{π}{4})

Use the following property:

sin (- x) = - sin (x)

sin (- \frac{π}{4}) = - sin (\frac{π}{4})

= cos (- \frac{π}{4}) - sin (\frac{π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{π}{4}) = cos (\frac{π}{4})

= cos (\frac{π}{4}) - sin (\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}

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

sin (\frac{π}{4})

sin (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} sin (x) 0 \frac{1}{2} \frac{2}{2} \frac{3}{2} 1 \frac{3}{2} \frac{2}{2} \frac{1}{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} sin (x) 0 - \frac{1}{2} - \frac{2}{2} - \frac{3}{2} - 1 - \frac{3}{2} - \frac{2}{2} - \frac{1}{2}

= \frac{2}{2}

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

Simplify

= 0

arctan (2) (\frac{6}{8})

0.625 - cos (0.625)

\frac{2 0 ^{2} \cdot sin ^{2} ( 5 3 ^{\circ} )}{20}

1 - cos (4 5^{\circ})

e^{0} cos (\frac{π}{2})

What is the value of cos(-pi/4)+sin(-pi/4) ?
The value of cos(-pi/4)+sin(-pi/4) is 0