Question

How to evaluate arccot -1

Answer 1

Do you know what arccot is?

Answer 2

1/tan x?

Answer 3

\[1/\tan (x)\] is just cot. Arccot is the inverse function of cot, or \[\tan ^{-1}(1/x)\]I'm assuming in this scenario you are allowed to use your calculator?

Answer 4

Oh, okay. thank you. No, I have to find the exact value in radians.

Answer 5

Okay, we can work with that, but it will be a bit more work.

It requires some knowledge of trigonometry and the special triangles (45-45-90 and 30-60-90).

Do you know what values of x where tan(x)=-1.

Answer 6

Alright. No, I'm afraid not. Can you please walk me through it?

Answer 7

Okay. The tan(x) is the sin(x) divided by the cos(x). In order for the value of tan(x) to be negative one, the sin(x) or the cos(x) must equal negative one, where the then must equal one.

The sin(45) equals 1/sqrt(2).
The cost(45) equals the same thing.

It then follows that tan(x) equals one. In order to get this to equal negative, we need to find an angle where either the sin(45) is negative one and cos(x) is one, or vise-versa.

By using the mnemonic All Students Take Calculus, we see that in Q4 cosine is positive while sine is negative.

Is there some value in the quadrant where tan(x) equals negative one?

Answer 8

Wouldn't it be (sqrt 2/2, negative sqrt 2/2)?

Answer 9

Those are the same as 1/sqrt(2). Multiply the expression by sqrt(2)/sqrt(2). You can use your calculator to verify this.

Answer 10

Okay. Thank you very much.

Answer 11

No prob. Let me know if you have any other questions. I know that wasn't the best explanation. I apologize for that.

Answer 12

No, it was very helpful. I was completely lost, thank you so much for you help.

Answer 13

:)