Question

What is the exact value of Cosine StartFraction 7 pi Over 12 EndFraction?

Answer 1

d

Explanation:

just did it on ed

Answer 2

`(1)/(4)` (
`√(2)` -
`√(6)` )

Explanation:

Using the addition formula for cosine

cos(a + b) = cosacosb - sinasinb

and the exact values

cos
`(\pi )/(3)` =
`(1)/(2)`, sin
`(\pi )/(3)` =
`(√(3) )/(2)` , cos
`(\pi )/(4)` = sin
`(\pi )/(4)` =
`(√(2) )/(2)`

Note
`(7\pi )/(12)` =
`(\pi )/(3)` +
`(\pi )/(4)` , thus

cos
`(7\pi )/(12)` = cos(
`(\pi )/(3)` +
`(\pi )/(4)` )

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

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

=
`(√(2) )/(4)` -
`(√(6) )/(4)`

=
`(1)/(4)` (
`√(2)` -
`√(6)` )