Find the exact value of sin (w/2), cos (w/2), and tan (w/2) using the half-angle formulas WITH the following data: sin w = (12/13), pi/2
I already have the answer, but I do not know how to do the problem. For me, this is the most important part. Can someone please walk me through every step, no matter how minor, to explain to me how to arrive at the answer. Any help is appreciated. Thank you.
I already have the answer, but I do not know how to do the problem. For me, this is the most important part. Can someone please walk me through every step, no matter how minor, to explain to me how to arrive at the answer. Any help is appreciated. Thank you.
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If sin w = 12/13, then cos w = 5/13.
If π/2 < w < π, then π/4 < w/x < π/2.
sin (w/2) = √((1 - 5/13)/2) = √((8/13)/2) = √(4/13) = 2/√13 = 2√13/13
cos (w/2) = √((1 + 5/13)/2) = √((18/13)/2) = √(9/13) = 3/√13 = 3√13/13
tan (w/2) = (2/√13)/(3/√13) = 2/3
If π/2 < w < π, then π/4 < w/x < π/2.
sin (w/2) = √((1 - 5/13)/2) = √((8/13)/2) = √(4/13) = 2/√13 = 2√13/13
cos (w/2) = √((1 + 5/13)/2) = √((18/13)/2) = √(9/13) = 3/√13 = 3√13/13
tan (w/2) = (2/√13)/(3/√13) = 2/3