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

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

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cos(pi+pi/4)

cos (π + \frac{π}{4})

- \frac{2}{2}

Solution steps

cos (π + \frac{π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{π}{4}) = \frac{2}{2}

= (- 1) \frac{2}{2} - 0 \cdot \frac{2}{2}

Simplify

= - \frac{2}{2}

cos^{2} (6 0^{\circ}) \cdot 44.8

sin (4 5^{\circ}) + sin (3 0^{\circ})

cos (- \frac{17 π}{6})

cot (- 6)

cos (arctan (\frac{8}{15}) - arccos (\frac{3}{5}))