For each ratio find exact values of the other two primary ratios.Each angle is i
ID: 3091235 • Letter: F
Question
For each ratio find exact values of the other two primary ratios.Each angle is in standard position with its terminal arm in theindicated quadranti) sin = 3/10 (QII)
ii) tan = 0.75 (QI)
iii) sin = -9/41 (QIV)
Explanation / Answer
i) sin = 3/10, QII For a right triangle, sin = length of opposite side / length ofhypotenuse => length of opposite side = 3 and length ofhypotenuse = 10 => length of adjacent side = sqrt( (10)^2 -(3)^2 ) = sqrt(10 - 9) = sqrt(1) = 1 Then cos = length of adjacent side / length ofhypotenuse = 1/10 and tan = length of opposite side / length ofadjacent side = 3/1 = 3 If is in the second quadrant, cos will be negative,sin will be positive, and tan , which equals sin / cos , will be negative, so the final answer is cos = -1/10 and tan =-3 ii) tan = .75 = 3/4, QI For a right triangle, tan = length of opposite side / length ofadjacent side => length of opposite side = 3 and length ofadjacent side = 4 => length of hypotenuse = sqrt( (3)^2 + (4)^2 ) =sqrt(9 + 16) = sqrt(25) = 5. Then cos = length of adjacent side / length ofhypotenuse = 4/5 and sin = length of opposite side / length ofhypotenuse = 3/5 When is in the first quadrant, cos will be positive,sin will be positive, and tan , which equals sin / cos , will be positive, so the final answer is cos = 4/5 and sin = 3/5 iii) sin = -9/41, QIV For a right triangle, sin = length of opposite side / length ofhypotenuse => length of opposite side = 9 and length ofhypotenuse = 41 => length of adjacent side = sqrt( (41)^2 - (9)^2 )= sqrt(1681 - 81) = sqrt(1600) = 40 Then cos = length of adjacent side / length ofhypotenuse = 40/41 and tan = length of opposite side / length ofadjacent side = 9/40 When is in the fourth quadrant, cos will be positive,sin will be negative, and tan , which equals sin / cos , will be negative, so the final answer is cos = 40/41 and tan = -9/40 If you find this post helpful, please rate it.
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