What is the value of cos(-(7pi)/4) ?

The value of cos(-(7pi)/4) is (sqrt(2))/2

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cos(-(7pi)/4)

cos (- \frac{7 π}{4})

\frac{2}{2}

Solution steps

cos (- \frac{7 π}{4})

Use the following property:

cos (- x) = cos (x)

cos (- \frac{7 π}{4}) = cos (\frac{7 π}{4})

= cos (\frac{7 π}{4})

Rewrite using trig identities:

cos (π) cos (\frac{3 π}{4}) - sin (π) sin (\frac{3 π}{4})

= cos (π) cos (\frac{3 π}{4}) - sin (π) sin (\frac{3 π}{4})

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

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

Simplify

= \frac{2}{2}

cot (\frac{5 π}{6})

sin (θ) = - \frac{4}{5}

arcsin (\frac{2}{2})

cot (\frac{5 π}{3})

sin (x) + cos (x) = 1