Question

How do you find the value of `cot 300^@`?

Answer 1

To find the value of `cot300`, you will first need to write the angle as the sum of difference of two angles, one of which is either `90^@, 180^@, 270^@ or 360^@`.

Note: Remember that when you write it with `90^@ or 270^@`, the fuction will change to it's co-function, in this case, to `tan`.

Let's first look at the two easiest ways to write this:

`cot300^@=cot(270+30)^@`

and

`cot300^@=cot(360-60)^@`

---

An important thing to remember is in which quadrants will a trigonometric function be positive. Here's an illustration:

Here,
A stands for all.
S stands for sin.
T stands for tan.
C stands for cos.

This means that
all fuctions are positive in the first quadrant,
the sin function and it's co-function csc are positive in the second quadrant,
the tan function and it's co-function cot are positive in the third quadrant,
the cos function and it's co-function sec are positive in the fourth quadrant.

One way to remember this arrangement is to recite the sentence:

`A`ll `S`tudents `T`ake `C`alculus.
This tells us which function would be positive in which quadrant.

I personally like to use the sentence
`A`ll `S`cience `T`eachers are `C`razy.

---

So, let's solve using the first equation.

`cot300^@=cot(270+30)^@`

The angle is greater than `270^@` and thus lies in the fourth quadrant. `tan` and `cot` are not positive here, i.e., they are negative.

Also, since you've used `270^@`, you need to change it to `tan`.

`cot300^@=cot(270+30)^@=-tan30^@`

`cot300^@=-1/sqrt3`

---

Now, let's solve the second equation.

`cot300^@=cot(360-60)^@`

Here, the angle is expressed with `360^@`, you must keep the function as `cot` itself. Again, the angle lies in the fourth quadrant, which means it is negative.

`cot300^@=cot(360-60)^@=-cot60^@`

`cot300^@=-1/sqrt3`