Question #139914
Determine the exact value of each trigonometric ratio

a) sin 75 degree
b) tan 5pie over 12
c) sin -pie over 12
1
Expert's answer
2020-10-29T15:33:22-0400

a)sin(75o) = sin(30o + 45o) = sin(30o)*cos(45o) + sin(45o)*cos(30o) = (1/21/2)*(2/2\sqrt2/2 ) + (2/2)3/2)(\sqrt2/2)*\sqrt3/2) = (2/2)((1+3)/2)=0.9659(\sqrt2/2)*((1+\sqrt3)/2) = 0.9659


b)tan(5*π\pi/12) = tan(3*π\pi/12 + 2*π\pi/12) = tan(π\pi/4 + π\pi/6) = (tan(π\pi/4) + tan(π\pi/6))/(1-tan(π\pi/4)*tan(π\pi/6)) = (1+1 +3/3\sqrt3/3)/(113/3))/(1-1*\sqrt3/3) = 3.732


c)sin(-π\pi/12) = sin(2π\pi/12 - 3π\pi/12) = sin(2π\pi/12)*cos(3π\pi/12) - sin(3π\pi/12)*cos(2π\pi/12) =

sin(π\pi/6)*cos(π\pi/4) - sin(π\pi/4)*cos(π\pi/6) = (1/2)(2/2)(2/2)(3/2)=(2/2)(13)=0.5176(1/2)*(\sqrt2/2) - (\sqrt2/2)*(\sqrt3/2) = (\sqrt2/2)*(1-\sqrt3) = -0.5176

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