find the exact value: sin[arccos(3^(1/2) / 4]

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hala718's profile pic

hala718 | High School Teacher | (Level 1) Educator Emeritus

Posted on

sin(arccos(3^(1/2)/4]

We will simplify starting from inside of the brackets out.

Let us rewrite 3^/12.

We know that .............

3^1/2 = 1.7321

==> 3^1/2 / 4 = 0.4230.

==> arccos(3^1/2)/4 =  64.34 degrees

==> sin[arccos(3^/12)/4 ] = sin 64.34 = 0.9014

Then the answer is:

sin[arccos(3^1/2)/4] = 0.9014 ( approx.)

giorgiana1976's profile pic

giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted on

We'll use the formula that:

sin(arccos x) = sqrt(1 - x^2) (1)

We'll put x = sqrt3/4

We'll raise to square both sides:

x^2 = 3/16

We'll substitute x in the expression (1):

sin(arccos sqrt3/4) = sqrt(1 - 3/16)

sin(arccos sqrt3/4) = sqrt[(16-3)/16]

sin(arccos sqrt3/4) = (sqrt13)/4

sin(arccos sqrt3/4) = 0.9013

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