Question
IF delta SIN=12/13
find the other five trigonometric functions value of delta
find the other five trigonometric functions value of delta
Answers
Bosnian
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
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
Reiny
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
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