Question

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.

Answer 1

so, do you know the identities ?

Answer 2

no ?

Answer 3

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

Answer 4

you can directly find cos alpha from there.

Answer 5

then all other ratios are just one step away!

tan = sin/cos
cot = cos /sin or 1/tan
sec = 1/cos
cosec = 1/ sin

Answer 6

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 \(\sqrt{3^2-1^2}=\sqrt{8}=2\sqrt{2}\)

Answer 7

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