What is the value of cos(3pi(0.25)+(pi)) ?

The value of cos(3pi(0.25)+(pi)) is (sqrt(2))/2

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cos(3pi(0.25)+(pi))

cos (3 π (0.25) + (π))

\frac{2}{2}

Solution steps

cos (3 π (0.25) + (π))

= cos (3 π \frac{1}{4} + π)

Rewrite using trig identities:

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

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

Use the following trivial identity:

cos (\frac{3 π}{4}) = - \frac{2}{2}

Use the following trivial identity:

cos (π) = (- 1)

Use the following trivial identity:

sin (\frac{3 π}{4}) = \frac{2}{2}

Use the following trivial identity:

sin (π) = 0

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

Simplify

= \frac{2}{2}

cos (\frac{19 π}{2})

tan (14 0^{\circ})

arccos (\frac{0}{1})

sin (18 1^{\circ})

sec (\frac{5 π}{12})

What is the value of cos(3pi(0.25)+(pi)) ?
The value of cos(3pi(0.25)+(pi)) is (sqrt(2))/2