Question

Find value of: cot^-1 (4)
(inverse of cotangent)
Why do we have to use cosine to evaluate this? Can someone explain clearly please? Why not just put the inverse of cot into the calculator?

Answer 1

@MathCurious are you here?

Answer 2

i am here? Could you help me?

Answer 3

We need to find the angle. Does your text mentions to use cosine?

Answer 4

What I understand is I have to use the given values from the Cotangent to find the hyp. then use the Cosine function. The only mention of this the text makes is because they have the same domain [0,pi) but I don't see why I can't just use cotangent in my calculator? I have to evaluate it using Cosine.

Answer 5

Even if we find cosine, we can't find angle without a trigonometric table or calculator.
Do you have a trigonometric table for cosine or sin

Answer 6

According to the cot the X and Y are given. So if cot (theta) = 4
X=4
Y=1

Answer 7

it's becaus cot, sec and cosec are not in calculators. First we need to find cosine and then we can find using calculator

Answer 8

but isn't cot just 1 / tan
?
calculators have tangent.

Answer 9

we could do that too :)

Answer 10

If we use cosine it is (\[4\sqrt{17}\div17\]
This isn't the same as the inverse cotangent of 4.So we cannot use 1 / tan

Answer 11

no it'd be
\[\cos^{-1} \frac {4}{\sqrt {17}}\]

Answer 12

we can use tan, no problem with that

Answer 13

according to my book and homework it is cos-1 (4 sqrt(17) / 17 )
You have to rationalize the denominator. I have the correct answer, i am just not clear on why it is this way. if you took 1/tan-1(4) you'd ge ta totally different value. hmm..

Answer 14

Google these two
"arccos (4 sqrt 17 /17) in degrees"
"arctan ( 1/4) in degrees"
Both will give you the same result

Answer 15

arc cos= inverse cosine

Answer 16

In google I got different numbers, unfortunately.The question calls for radians

Answer 17

Ok I added the "in degrees' and got the same for degrees. I must be doing something wrong on my calculator? haha. because 1 / tan-1(4) does not yield the same results..

Answer 18

yes, it's tan-1 (1/4)

Answer 19

\[\cot^{-1} (4)\ne \frac{1}{\tan^{-1} 4}\]
\[\cot^{-1} (4)= \tan^{-1} \frac 1{4}\]

Answer 20

Oooh. How did you come up with this? if tan = y/x then...
1 / y/x = x/y.

So why doesn't cot = 1 / tan ???

I am so confused, but it's probablyu so simple!

Answer 21

Just a moment, I'll explain you

Answer 22

let "a" be the angle
\[\tan a=\frac {x}{y}\]
\[\cot a =\frac {y}{x}\]
hence
\[a=\cot^{-1} \frac {y}{x}\]
from the first expression
\[a=\tan^{-1}\frac{x}{y}\]

Answer 23

Okay, it's so simple! Thank you so much for your help. Medal!

Answer 24

Welcome :D