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

1 Answer
Dec 9, 2014

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:

enter image source here

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:

All Students Take Calculus.
This tells us which function would be positive in which quadrant.

I personally like to use the sentence
All Science Teachers are Crazy.


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