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Mathematics 80 Online
OpenStudy (anonymous):

Assume that 0 < α < π/2 and that sin α = 1/3. Find the values of the other five trig functions of α. Use identities and do this by hand.

hartnn (hartnn):

so, do you know the identities ?

hartnn (hartnn):

no ?

hartnn (hartnn):

know this \(\huge \sin^2x+\cos^2x=1\)

hartnn (hartnn):

you can directly find cos alpha from there.

hartnn (hartnn):

then all other ratios are just one step away! tan = sin/cos cot = cos /sin or 1/tan sec = 1/cos cosec = 1/ sin

OpenStudy (anonymous):

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OpenStudy (anonymous):

there is a picture of an angle \(\alpha\) where \(\sin(\alpha)=\frac{1}{3}\) you need the other side which you get via pythagoras it will be \(\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}\)

OpenStudy (anonymous):

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OpenStudy (anonymous):

now you can compute all the other ratios for example \[\cos(\alpha)=\frac{2\sqrt{2}}{3}\]

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