find the value of sin 75°and cos 75°
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Answer:
Therefore, the requested values for sin 75 and cos 75 are: sin 75 = (sqrt 2 + sqrt6)/4 and cos 75 = (sqrt6 - sqrt2)/4.
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Step-by-step explanation:
The values of sin 45, sin 30, cos 45 and cos 30 are commonly known. We use these to determine the value of cos 75 and sin 75.
Use the relation cos (x + y) = (cos x)*(cos x) - (sin x)(sin y)
cos 75 = cos (30 + 45)
=> (cos 30)(cos 45) - (sin 30)(sin 45)
cos 30 = sqrt(3) /2, sin 30 = 1/2, sin 45 = cos 45 = 1/sqrt(2)
=>sqrt(3) /2sqrt(2) - 1/2*sqrt(2)
=>[sqrt(3) - 1]/2sqrt(2)
Use the relation sin(x + y) = sin x * cos y + sin y *cos x
sin (45 + 30) = (1/sqrt 2 )(sqrt 3 /2) + (1/ 2 )(1/sqrt 2 )
=> (1 + sqrt 3 )/sqrt 8
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