Question

Question #048a8

Answer 1

1

Explanation:

`sin(a)=-(sqrt(65)/65)`

Get the arcsine

`A=sin^-1(-sqrt(65)/65)`

`A=-7.125^o`

But angle A is on quadrant III

Get coterminal angle

`360-7.125=352.875`

Get reference angle

`360-352.875=7.125`

Get angle on Quadrant III

`180+7.125=187.125`

Test A if derived angle is correct

`sin(-7.125)=-0.124`
`sin(187.125)=-0.124`

Use angle A for half angle identity of cosine

`cos(A/2)` `= sqrt((1+cos(187.125))/2)`

Resulting to

=`0.998 ~= 1`