Question

If f(x) =sin x and f(a) =¾ find the value of f(a) +5f(-a)

Answer 1

The sine function is an odd function, that is, it has the following property:

`f(-x)=-f(x)`

Using this property, we can find the value of f(-a):

`\begin{gathered} f(a)=(3)/(4) \\ f(-a)=-f(a)=-(3)/(4) \end{gathered}`

Now we can calculate the value of the expression:

`f(a)+5f(-a)=(3)/(4)+5\cdot(-(3)/(4))=(3)/(4)-(15)/(4)=-(12)/(4)=-3`