IF delta SIN=12/13

Question

find the other five trigonometric functions value of delta

Answer 1

If delta SIN=12/13 mean:

sin Δ = 12 / 13

Then:

cos Δ = ± √ ( 1 - sin² Δ )

cos Δ = ± √ [ 1 - ( 12 / 13 )² ]

cos Δ = ± √ [ 1 - ( 144 / 169 ) ]

cos Δ = ± √ ( 169 / 169 - 144 / 169 )

cos Δ = ± √ ( 25 / 169 )

cos Δ = ± 5 / 13

tan Δ = ± sin Δ / cos Δ

tan Δ = ± ( 12 / 13 ) / ( 5 / 13 ) = ± ( 12 * 13 ) / ( 5 * 13 ) = ± 12 / 5

cot Δ = ± cos Δ / sin Δ = ± ( 5 / 13 ) / ( 12 / 13 ) = ± ( 5 * 13 ) / ( 12 * 13 ) = ± 5 / 12

sec Δ = ± 1 / cos Δ = ± 13 / 5

csc Δ = ± 1 / sin Δ = ± 13 / 12

Answer 2

you have to consider the CAST rule

using Bosnians answers, we have to eliminate some of the ± cases

since sin Δ = 12 / 13
Δ could be in quadrants I or II

in quad I
sinΔ= 12/13 , cscΔ = 13/12
cosΔ = 5/13 , secΔ = 13/5
tanΔ = 12/5 , cotΔ = 5/12

in quad II
sinΔ = 12/13 , cscΔ = 13/12
cosΔ = -5/13 , secΔ = -13/5
tanΔ = -12/5 , cotΔ = -5/12