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Evaluate using the Pythagorean identities.
Find sinθ and cosθ if tanθ = 1/4 and sinθ >0
3 answers
Arora gave you a detailed solution to this type of question here:
https://www.jiskha.com/display.cgi?id=1516371278
follow the same steps, and stick to one name
https://www.jiskha.com/display.cgi?id=1516371278
follow the same steps, and stick to one name
well I suppose but I prefer the triangle
tan T = 1/4
but we know
tan^2 T + 1 = sec^2 T
so
1/16 + 1 = 1/cos^2 T
17/16 = 1/cos^2 T
so
cos^2 T = 16/17
take the square root now
then for the sin
sin^2 T = 1 - 16/17 = 1/17
take the square root now
===========================
check
T = tan^-1 .25
T = 14.04 deg
then
sin T = .243
sin^2 T = .0588
and 1/17 = .0588 so it worked
tan T = 1/4
but we know
tan^2 T + 1 = sec^2 T
so
1/16 + 1 = 1/cos^2 T
17/16 = 1/cos^2 T
so
cos^2 T = 16/17
take the square root now
then for the sin
sin^2 T = 1 - 16/17 = 1/17
take the square root now
===========================
check
T = tan^-1 .25
T = 14.04 deg
then
sin T = .243
sin^2 T = .0588
and 1/17 = .0588 so it worked