Answer:
sin(-a)= -15 /17
Step-by-step explanation:
Alright, lets remember that sin(x) is odd function, which means that
wherever you watch an expression like this: sin(-a), you can use the odd functions property, and turn it like the following
sin(-a)= - sin(a)
Now, other thing to remember: [tex](sin(x))^{2}+(cos(x))^{2}=1[/tex]
So, we can obtain any value for sin(x) function starting from the opposite function, cos(x), using the following:
[tex]sin(x)=\sqrt{1-(cos(x))^{2} }[/tex]
So, if cos(a)= - 8 / 17, using the above equation we obtain the value for sin(a)
[tex]sin(a)=\sqrt{1 - (cos(a))^{2} } = \sqrt{1 - ( \frac{8}{17} )^{2} }= \sqrt{\frac{225}{289} } =15/17[/tex]
Using the odd function property, we get the following result
sin(-a)= - sin(a) = -15/17
