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Calculate the expression sin(arcsin1/2)+sin(arccos scuare root 3/2).

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pavelpimen | Student, Undergraduate | (Level 3) Honors

Posted July 6, 2011 at 12:06 AM via web

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Calculate the expression sin(arcsin1/2)+sin(arccos scuare root 3/2).

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giorgiana1976 | College Teacher | (Level 3) Valedictorian

Posted July 6, 2011 at 12:10 AM (Answer #1)

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We'll recall the fact that sin (arcsin x) = x and sin (arccos x) = sqrt(1 - x^2)

Comparing, we'll get:

sin (arcsin(1/2))= 1/2 (1)

sin (arccos (sqrt3)/2) = sqrt[1 - (3/2)^2]

sin (arccos (sqrt3)/2) = sqrt (1 - 3/4)

sin (arccos (sqrt3)/2) = sqrt [(4-3)/4]

sin (arccos (sqrt3)/2) = sqrt (1/4)

sin (arccos (sqrt3)/2) = 1/2 (2)

We'll add (1) + (2):

sin (arcsin(1/2)) + sin (arccos (sqrt3)/2) = 1/2 + 1/2

sin (arcsin(1/2)) + sin (arccos (sqrt3)/2) = 1

The value of the given expression is sin (arcsin(1/2)) + sin (arccos (sqrt3)/2) = 1.

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justaguide | College Teacher | (Level 2) Distinguished Educator

Posted July 6, 2011 at 12:20 AM (Answer #2)

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We have to find sin(arc sin(1/2)) + sin(arc cos (sqrt 3/2)

arc sin(1/2) = 30 degrees

arc cos(sqrt 3 / 2) = 30 degrees

sin(arc sin(1/2)) + sin(arc cos (sqrt 3/2)

=> sin 30 + sin 30

=> 2*sin 30

sin 30 = 1/2

=> 2*(1/2)

=> 1

The value of sin(arc sin(1/2)) + sin(arc cos (sqrt 3/2) = 1

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