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

What's the exact value of sin 7/12?-example-1
User Elbowich
by
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2 Answers

15 votes
15 votes
The exact value of sin(7π12) sin ( 7 π 12 ) is √2+√64 2 + 6 4 .
User Amit Patel
by
2.6k points
15 votes
15 votes

Answer:

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)

User Vlad Gincher
by
3.4k points