Find the values of the trigonometric functions of t from the

Find the values of the trigonometric functions of t from the given information. Noles Ask Yeur Teacher csc(t)7, cos(e) sin(t) . cos(t) tan(t) sec(t) cot(e) Noed Holp? Rout 30. t points SAigTrig4 5 2 059 My Notes four tea A man is lying on the beach, flying a kite. He holds the end of the kite string at ground level and estimates the angle of elevation of the kite to be 65, If the string is 500 ft long, how high is the kite above the ground? (Round your answer to the nearest foot.) ft ft Need Help? Readin wWach

Solution

given cot(theta) = - 5/8

cot(theta) = cos(theta) / sin(theta) , cos(theta) > 0, sin(theta) has to be < 0

cot(theta) = adjacent side / opposite side

by pythogorous theorem

hyp^2 = adj^2 + opp^2

hyp^2 = (8)^2 + ( -5)^2 ==> 64 + 25

hyp= sqrt(89)

sin(theta) = opp / hyp ==> - 5 / sqrt(89)

cos(theta) = adj / hyp ==> 8 / sqrt(89)

tan(theta) = opp / adj =sin(theta) /cos(theta) = 1/cot(theta) ==> - 8 / 5

csc(theta) = 1/sin(theta)= - sqrt(89) / 5

sec(theta) = 1/cos(theta) = sqrt(89) / 8

====

csc(t) = 7 , cos(theta) < 0

sin(t) = 1/csc(t) ==> 1/7 ==> opp / hyp

hyp^2 = adj^2 + opp^2

7^2 = adj^2 + 1^2

adj^2 = 49 - 1

adj= + / - sqrt(48)

cos(theta) = adj / hyp = - sqrt(48) / 7

sec(theta) = 1/cos(theta) = - 7 / sqrt(48)

tan(theta) = sin(theta) /cos(theta) = - 1 / sqrt(48)

cot(theta) = 1/tan(theta) = - sqrt(48) / 1