What is expand 3sin(pi/4 (x-5))+5 ?

The solution to expand 3sin(pi/4 (x-5))+5 is -(3sin((pix)/4))/(sqrt(2))+(3cos((pix)/4))/(sqrt(2))+5

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expand 3sin(pi/4 (x-5))+5

expand

3 sin (\frac{π}{4} (x - 5)) + 5

- \frac{3 sin ( \frac{π x}{4} )}{2} + \frac{3 cos ( \frac{π x}{4} )}{2} + 5

Solution steps

3 sin (\frac{π}{4} (x - 5)) + 5

3 sin (\frac{π}{4} (x - 5)) = \frac{- 3 2 sin ( \frac{π x}{4} ) + 3 2 cos ( \frac{π x}{4} )}{2}

= \frac{3 2 cos ( \frac{π x}{4} ) - 3 2 sin ( \frac{π x}{4} )}{2} + 5

Apply the fraction rule:

\frac{a \pm b}{c} = \frac{a}{c} \pm \frac{b}{c}

\frac{- 3 2 sin ( \frac{π x}{4} ) + 3 2 cos ( \frac{π x}{4} )}{2} = - \frac{3 2 sin ( \frac{π x}{4} )}{2} + \frac{3 2 cos ( \frac{π x}{4} )}{2}

= - \frac{3 2 sin ( \frac{π x}{4} )}{2} + \frac{3 2 cos ( \frac{π x}{4} )}{2} + 5

Cancel

\frac{3 2 sin ( \frac{π x}{4} )}{2} : \frac{3 sin ( \frac{π x}{4} )}{2}

= - \frac{3 sin ( \frac{π x}{4} )}{2} + \frac{3 2 cos ( \frac{π x}{4} )}{2} + 5

Cancel

\frac{3 2 cos ( \frac{π x}{4} )}{2} : \frac{3 cos ( \frac{π x}{4} )}{2}

= - \frac{3 sin ( \frac{π x}{4} )}{2} + \frac{3 cos ( \frac{π x}{4} )}{2} + 5

\frac{\partial}{\partial x} ((z) (x^{3} z^{5} + sin (y^{7} z^{5}) + 6))

3 (3 d - 4 e) + 2 (d - 5 e)

\frac{1}{x \cdot ( x ^{2} + 1 )}

3 sin (\frac{π}{12} (t - 6)) + 13

\frac{2 x ^{3} + x ^{2} + 5 x - 2}{( x ^{2} + 1 ) ( x ^{2} + 4 )}

What is expand 3sin(pi/4 (x-5))+5 ?
The solution to expand 3sin(pi/4 (x-5))+5 is -(3sin((pix)/4))/(sqrt(2))+(3cos((pix)/4))/(sqrt(2))+5