If sine theta=5/7 and lies in quadrant 2. how do i find the other leg to get the other 5 trig functions?

Answer 1

sin is 5/7

sin is opposite/hyptenuse

following the pythagorean theorem the adjacent side is sqrt 14

Now you have opposite/hypotenuse/adjacent. You just need to use SOHCAHTOA to figure the answers out now.

Also, csc is the inverse of sin, sec is the inverse of cos and cot is the inverse of tan.

Answer 2

sine theta=5/7 and lies in quadrant 2

other leg x (base), x^2= 7^2 - 5^2= 49 - 25 = 24
This implies x = minus of sqrt(24) = - 2sqrt(6)
now hyp. = 7 opp. side = 5 and base = - 2sqrt(6)
one can find all others trig functions

Answer 3

Take a right angled triangle ABC, where m
let sin A = 5/7 = opposite side /hypotenuse

so opposite side = 5

hypotenuse = 7

adjacent side = sqrt(hypotenuse^2 - opposite side ^2)

adjacent side = sqrt(49 - 25) = sqrt(24) = 2 sqrt6)

since A is in 2nd quadrant , only sin and csc are positive and all others trig functions are negative.

cosA = adjacent side/hypotenuse = - 2sqrt(6)/7

tan A = sinA/cosA = (5/7)*7/2sqrt(6) = - 5/2 sqrt(6)

csc A = 1/sinA = 7/5

secA = 1/cosA = - 7/2 sqrt(6)

cotA = 1/tanA = -2 sqrt(6)/5

Answer 4

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