Asked by Anonymous
If sin(theta) = 3/7, what is sin (pi/2 - theta)?
Answers
Answered by
Reiny
If sinØ = 3/7,
y=3 , r = 7 and x^2 + 3^2 = 7^2
x = ± √40
Ø could be in I or II
if Ø is in I
sinØ = 3/7
cosØ = √40/7
cos(π/2 - Ø) = cos π/2 cosØ + sin π/2 sinØ
= 0 + sinØ
= 3/7
If Ø is in II
sinØ = 3/7
cosØ = -√40/7
cos(π/2 - Ø) = cos π/2 cosØ + sin π/2 sinØ
= 0 + sinØ
= 3/7
Of course we should have seen that this is just using one of the basic trig identities
sin x = cos(π/2 - x)
y=3 , r = 7 and x^2 + 3^2 = 7^2
x = ± √40
Ø could be in I or II
if Ø is in I
sinØ = 3/7
cosØ = √40/7
cos(π/2 - Ø) = cos π/2 cosØ + sin π/2 sinØ
= 0 + sinØ
= 3/7
If Ø is in II
sinØ = 3/7
cosØ = -√40/7
cos(π/2 - Ø) = cos π/2 cosØ + sin π/2 sinØ
= 0 + sinØ
= 3/7
Of course we should have seen that this is just using one of the basic trig identities
sin x = cos(π/2 - x)
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