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Given cos (central angle) = 2/3 and sin (central angle) >0, find cot central angle?
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Given cos (central angle) = 2/3 and sin (central angle) >0, find csc central angle
1 Answer
- Meng tianLv 78 years ago
cos(c. a.) = 2/3
sin(c. a.) > 0, which implies c. a. is in 1st quadrant
adjacent side = 2
hypotenuse = 3
opposite side = sqrt(3^2 - 2^2) = sqrt(9 - 4) = sqrt(5)
sin(c. a.) = opposite side / hypotenuse = sqrt(5) / 3
cot(c. a.) = cos(c. a.) / sin(c. a.) = [2 / 3] / [sqrt(5) / 3] = 2/sqrt(5)
csc(c. a.) = 1 / sin(c. a.) = 1 / [sqrt(5) / 3] = 3/sqrt(5)