How to find out the sin value from cos

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Homework Statement

we know α ∈ [0, π] and cos α = √5/3, what is the exact value of sin α and the approx. angle of sin α?

Relevant Equations

sin[sup]2[/sup] α + cos[sup]2[/sup] α = 1, unit circle

First off sorry if something doesn't make sense, english is not my native language.

I know i should start with sin² α + cos² = 1, but ant really continue from it.
i am being confused by cos α = √5/3 since i know it isn't found in normal trig tables. So my problem is how to find out values of any radian value, and how to find out the corresponding value in sin?

 

[Orodruin]

I am not sure where your problem is. You do not need trigonometric tables because you are already given the value of the cosine of the angle and you have the trigonometric one, which includes the sine of the angle and the cosine of the angle. One known and one unknown. Solve for the unknown.

 

[Steve4Physics]

I am also not clear what your problem is. But a geometrical approach would be to sketch a right-angled triangle with one of its angles $\alpha$.

With appropriate sides of lengths $\sqrt 5$ and $3$, you have $\cos {\alpha} = \frac {\sqrt 5}3$. And take it from there.

Edit: The exact answer might (or might not) include a surd (square root).

The approximate answer should be the exact answer rounded to, say, 3 decimal places.

 

[rssvn]

I am also not clear what your problem is. But a geometrical approach would be to sketch a right-angled triangle with one of its angles $\alpha$.

With appropriate sides of lengths $\sqrt 5$ and $3$, you have $\cos {\alpha} = \frac {\sqrt 5}3$. And take it from there.

Edit: The exact answer might (or might not) include a surd (square root).

The approximate answer should be the exact answer rounded to, say, 3 decimal places.

i need the square root for sin(x)²=4/9, i may have overestimated the question at first

 

[Steve4Physics]

i need the square root for sin(x)²=4/9, i may have overestimated the question at first

You don't need a square root symbol in your exact answer because (of course) $\frac 49$ has an exact rational square root.

But if the question had said (for example) $\cos \alpha = \frac {\sqrt 7}3$, then your exact answer would require a square root symbol.

 

[DaveC426913]

surd

TIL.

(almost six decades on the planet - my first encounter)

 

[Steve4Physics]

TIL.

More than seven decades on the planet - and my first encounter!

 

[SammyS]

Have you ever heard of the "conjugate surd" ?

 

[BvU]

would that be the "turd" ?

 

[Steve4Physics]

Have you ever heard of the "conjugate surd" ?

I believe they were a heavy metal band from Manchester, back in the early 1970s.