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

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#