a)sin(75o ) = sin(30o + 45o ) = sin(30o )*cos(45o ) + sin(45o )*cos(30o ) = (1 / 2 1/2 1/2 )*(2 / 2 \sqrt2/2 2 /2 ) + ( 2 / 2 ) ∗ 3 / 2 ) (\sqrt2/2)*\sqrt3/2) ( 2 /2 ) ∗ 3 /2 ) = ( 2 / 2 ) ∗ ( ( 1 + 3 ) / 2 ) = 0.9659 (\sqrt2/2)*((1+\sqrt3)/2) = 0.9659 ( 2 /2 ) ∗ (( 1 + 3 ) /2 ) = 0.9659
b)tan(5*π \pi π /12) = tan(3*π \pi π /12 + 2*π \pi π /12) = tan(π \pi π /4 + π \pi π /6) = (tan(π \pi π /4) + tan(π \pi π /6))/(1-tan(π \pi π /4)*tan(π \pi π /6)) = (1 + 1 + 1 + 3 / 3 \sqrt3/3 3 /3 ) / ( 1 − 1 ∗ 3 / 3 ) )/(1-1*\sqrt3/3) ) / ( 1 − 1 ∗ 3 /3 ) = 3.732
c)sin(-π \pi π /12) = sin(2π \pi π /12 - 3π \pi π /12) = sin(2π \pi π /12)*cos(3π \pi π /12) - sin(3π \pi π /12)*cos(2π \pi π /12) =
sin(π \pi π /6)*cos(π \pi π /4) - sin(π \pi π /4)*cos(π \pi π /6) = ( 1 / 2 ) ∗ ( 2 / 2 ) − ( 2 / 2 ) ∗ ( 3 / 2 ) = ( 2 / 2 ) ∗ ( 1 − 3 ) = − 0.5176 (1/2)*(\sqrt2/2) - (\sqrt2/2)*(\sqrt3/2) =
(\sqrt2/2)*(1-\sqrt3) = -0.5176 ( 1/2 ) ∗ ( 2 /2 ) − ( 2 /2 ) ∗ ( 3 /2 ) = ( 2 /2 ) ∗ ( 1 − 3 ) = − 0.5176
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