Do I just add the two?

[indigo girder]

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[random urchin]

No, you need to recall the formulas for sine and cosine of sum.

[knotty sparrow]

wdym

[vocal lance]

change tag to alg

[knotty sparrow]

why?

[vocal lance]

because it's not calculus

[knotty sparrow]

this question is from a pre-calc practice test

[random urchin]

Still, this isn't calculus.

[vocal lance]

it can be considered precalc but definitely not calc

[knotty sparrow]

oh

how do i change tag

[random urchin]

Well, I was hoping you would just take a look in your textbook, but alright...
sin(α + β) = sin(α)cos(β) + cos(α)sin(β)
cos(α + β) = cos(α)cos(β) - sin(α)sin(β)

[knotty sparrow]

what about tan

[random urchin]

Well, as usual, tan(x) = sin(x)/cos(x).

But if you want the formula just for it:
tan(α + β) = (tan(α) + tan(β))/(1 - tan(α)tan(β))

[knotty sparrow]

ok one sec lemme do and show u

[knotty sparrow]

i did the sine one but i got some decimal

0.6914

[random urchin]

That's wrong. And don't round.

[knotty sparrow]

oh

[knotty sparrow]

Do we just do like this

[random urchin]

What? No.

We have cos(α) = √(5)/5, not cos(√(5)/5). You need to find α and β first.

[knotty sparrow]

oh

[random urchin]

After that, you will also need to use the following identities:
sin(arcsin(x)) = cos(arccos(x)) = x
sin(arccos(x)) = cos(arcsin(x)) = √(1 - x^2)

[knotty sparrow]

is a still a decimal

[random urchin]

Don't round, as I said. What did you get?

[knotty sparrow]

1.10714871

[random urchin]

I just said not to round...

What exact expression did you get?

[random urchin]

Um...

If you're not even trying to do it yourself, I am not going to help.

[knotty sparrow]

i did before it didnt work

so i tried this way

and it still didnt work

[random urchin]

Fine...
First of all, what did you get as the solution of cos(α) = √(5)/5, considering α is in the first quadrant?

[knotty sparrow]

im am confused

[random urchin]

What do you mean?

[knotty sparrow]

like the decimal one?

[random urchin]

No!

[knotty sparrow]

bruh im stupid

[random urchin]

Did the many times I told you not to round not say anything?

Why would you even round?

[knotty sparrow]

im so lost

[random urchin]

If that's the case, return to your textbook and practice solving elementary trigonometric equations first.

[vocal lance]

why are you solving cos(α) = √(5)/5 💀

[random urchin]

Hm. Well, true, we can get sin(α) without solving it.