^{rd}Quadrant where Sine is positive

^{st}Quadrant where cosine is positive

use the sum to product formula to find the exact value of

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Sum to Product formula for Sine function is

sin(u) + sin (v) = 2sin ((u+v)/2).cos ((u-v)/2)

Substitute u = http://11.pi/12 and v = http://7.pi/12 in above equation.

sin 11pi/12 + sin 7pi/12

=2sin((11pi/12+7pi/12)/2).cos((11pi/12-7pi/12)/2)

=2sin((18pi/12)/2).cos((4pi/12)/2)

=2sin((3pi/2)/2).cos((pi/3)/2)

=2sin(3pi/4).cos(pi/6) ....angle 3pi/4=135 degrees which is in 3^{rd} Quadrant where Sine is positive

....angle pi/6 = 30 degrees which is in 1^{st} Quadrant where cosine is positive

=2.(1/sqrt(2)).(sqrt(3)/2)

=sqrt(3/2)

= sqrt(1.5)

=1.225

Parviz F. | Mathematics professor at Community CollegesMathematics professor at Community Colle...

Sin 11∏/12 + Sin 7∏/ 12 =

Sin ( ∏/ 12) + Sin ( 6∏/12 + ∏/12) =

Sin ( ∏/4 - ∏/6) + Sin( ∏/4 + ∏/ 6)=

Sin ∏/4 . Cos ∏/6 - Sin ∏/6 cos ∏/4 + Sin ∏/4 cos ∏/6 + Sin∏/6 cos ∏/4 =

2 Sin ∏/4 . Cos ∏/6 =

2 √2 / 2 . √3 /2 = √6 / 2

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