SOLUTION: Use a half-angle formula to determine the value of the trigonometric functions. Answers must be in exact form, cannot have decimals.
how do you solve this:
sin(11π/8) =
Algebra ->
Trigonometry-basics
-> SOLUTION: Use a half-angle formula to determine the value of the trigonometric functions. Answers must be in exact form, cannot have decimals.
how do you solve this:
sin(11π/8) =
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You can put this solution on YOUR website! how do you solve this:
sin(11π/8) =
sin(π/8)=
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sin(11π/8)=(22π/8)/2=(11π/4)/2
sin half angle formula: sin s/2=±√[(1-cos s)/2]
sin (11π/4)/2=±√[1-cos(11π/4)/2] (select negative root because sin(11π/8) is in quadrant III where sin<0)
cos(11π/4)=-√2/2 in quadrant II where cos<0
√[1-cos(11π/4)/2]=√[(1-(-√2/2))/2]=√[(1+√2/2)/2]=√(2+√2)/2
sin(11π/8) =-√(2+√2)/2
..
sin(π/8)=(2π/8)/2=(π/4)/2
sin (π/4)/2=±√[1-cos(π/4)/2] (select positive root because sin(π/8) is in quadrant I where sin>0)
cos(π/4)=√2/2 in quadrant I where cos>0
√[1-cos(π/4)/2]=√[(1-√2/2)/2]=√(2-√2)/2
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