What is expand sin(10pi+(5pi)/4) ?

The solution to expand sin(10pi+(5pi)/4) is -(sqrt(2))/2

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expand sin(10pi+(5pi)/4)

expand

sin (10 π + \frac{5 π}{4})

- \frac{2}{2}

Decimal Notation

- 0.70710 \dots

Solution steps

sin (10 π + \frac{5 π}{4})

Simplify:

10 π + \frac{5 π}{4} = \frac{45 π}{4}

= sin (\frac{45 π}{4})

sin (\frac{45 π}{4}) = sin (\frac{5 π}{4})

= sin (\frac{5 π}{4})

Rewrite using trig identities:

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

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

Use the following trivial identity:

sin (π) = 0

Use the following trivial identity:

cos (\frac{π}{4}) = \frac{2}{2}

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

Simplify

= - \frac{2}{2}

\frac{π}{0}

\frac{s ^{2} + 2}{( s ^{2} + 1 ) ( s ^{2} + 6 )}

\frac{d}{d x} ((t) (cos (t) + 8 t + 2 sin (3 t)))

\frac{4 x y}{( x ^{2} + 1 ) ( y ^{2} + 1 )}

(1, 3) y (- 1, - 2)

What is expand sin(10pi+(5pi)/4) ?
The solution to expand sin(10pi+(5pi)/4) is -(sqrt(2))/2