Quick question on arctan(1)

[MegaScientifical]

Part of my calculus work requires me to calculate this. I am finding places telling me arctan(1)=x is tan(x)=1, but then they make the leap to "tan(pi/4)=1". I'm not sure how they are getting to this point. The explanations are a bit... confusing...

[Ad Bot]

[Texan101]

Tan(pi/4) = Sin(pi/4)/Cos(pi/4).
Sin(pi/4) = sqrt(2)/2.
Cos(pi/4) = sqrt(2)/2.
(sqrt(2)/2)/(sqrt(2)/2) = 1.
Therefore, Tan(pi/4) = 1.

[MegaScientifical]

Hmm... Thanks, that helps. Still confused, but looking over that... It makes me question she'd find that in our scope to know on this particular test. Not sure this won't be useful, just that I might have more time to understand it later on. I get what is going on, hyp/opp/adj etc. Just remembering how it works.

[Texan101]

Hmm... Thanks, that helps. Still confused, but looking over that... It makes me question she'd find that in our scope to know on this particular test. Not sure this won't be useful, just that I might have more time to understand it later on. I get what is going on, hyp/opp/adj etc. Just remembering how it works.

I'm kind of surprised she'd be going over how it works. I just learned it a little over a month ago, and I'm in college.

[MegaScientifical]

Well I'm in Calculus in college. We're getting derivatives of various things, including inverse sines, cosines, and tangents. Part of it also just went over what they would be instead of just the derivatives.

[Master Shadow Phoenix]

As long as you know your x, y, and r for your reference angles (30, 45, 60), and the positives for the six trigonometric functions in the four quadrants, then you should be fine.

[blazerblock2]

jesus christ i do not want to graduate

[MegaScientifical]

jesus christ i do not want to graduate

This isn't even college level, I think. It's just I haven't done straight math in two years. I mean, arctan(1) = x is tan(x) = 1, which should be somewhat basic in terms of its use.

[carolcat]

jesus christ i do not want to graduate

i don't think calculus is required in college

[Texan101]

This isn't even college level, I think. It's just I haven't done straight math in two years. I mean, arctan(1) = x is tan(x) = 1, which should be somewhat basic in terms of its use.

It is college-level. I wouldn't have had to pull out the unit circle otherwise.

[Bloody Mary]

Isn't arctan just tan^-1?

[Master Shadow Phoenix]

Isn't arctan just tan^-1?

Yes.

[ChexGuy331]

i don't think calculus is required in college

Depends on where you go.

[GhostStar]

Tan(pi/4) = Sin(pi/4)/Cos(pi/4).
Sin(pi/4) = sqrt(2)/2.
Cos(pi/4) = sqrt(2)/2.
(sqrt(2)/2)/(sqrt(2)/2) = 1.
Therefore, Tan(pi/4) = 1.

thats looks really scary.

[Kill All]

Isn't arctan just tan^-1?

arctan(x)=tan^-1(x)
[tan(x)]^-1=cot(x)