Asked by TEETEE
Use an Addition or Subtraction Formula to find the exact value of the expression.
Sin(−5π/12)
Sin(−5π/12)
Answers
Answered by
Reiny
some students have less difficulty if the angle is in degrees.
Let's try this approach ....
5π/12 radians = 75°
so sin(-5π/12)
= sin(-75°) which is in quadrant IV, making the sine negative
= -sin(75°)
= -sin(30° + 45°)
= -(sin30cos45 + cos30sin45)
= -( (1/2)(√2/2) + (√3/3)(√2/2) )
= - √2/4 - √6/4
so <b>sin(05π/12) = -√2/4 - √6/4</b>
check:
on my calculator:
sin(-5π/12) = -.9659...
and -√2/4 - √6/4 = -.9659..
My answer is correct
Let's try this approach ....
5π/12 radians = 75°
so sin(-5π/12)
= sin(-75°) which is in quadrant IV, making the sine negative
= -sin(75°)
= -sin(30° + 45°)
= -(sin30cos45 + cos30sin45)
= -( (1/2)(√2/2) + (√3/3)(√2/2) )
= - √2/4 - √6/4
so <b>sin(05π/12) = -√2/4 - √6/4</b>
check:
on my calculator:
sin(-5π/12) = -.9659...
and -√2/4 - √6/4 = -.9659..
My answer is correct
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