Question

What's the exact value of sin 7/12?

Answer 1

The exact value of sin(7π12) sin ( 7 π 12 ) is √2+√64 2 + 6 4 .

Answer 2

C

Explanation:

using the addition formula for sine

sin(A + B) = sinAcosB + cosAsinB

note that
`(7\pi )/(12)` =
`(\pi )/(3)` +
`(\pi )/(4)` , then

sin
`(7\pi )/(12)`

= sin(
`(\pi )/(3)` +
`(\pi )/(4)` )

= sin
`(\pi )/(3)`cos
`(\pi )/(4)` + cos
`(\pi )/(3)`sin
`(\pi )/(4)`

= (
`(√(3) )/(2)` ×
`(√(2) )/(2)` ) + (
`(1)/(2)` ×
`(√(2) )/(2)` )

=
`(√(6) )/(4)` +
`(√(2) )/(4)`

=
`(√(2)+√(6) )/(4)`