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How do you evaluate cot30?

Answer
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Hint: ' cot ' is the word used in trigonometry for cotangent which is the reciprocal of a tangent. The cotangent of an angle is also defined as the cosine of the angle divided by the sin of the angle. Therefore to find the cotangent of an angle we can either use the value of the tangent of that particular angle or cosine divided sine for that particular angle. So cotangent formula requires the study of the tangent of angles as it is the reciprocal of a tangent. There are a number of trigonometric formulas that can be used here.

Complete step by step solution:
Method 1:
We can find the value of cot 30 directly by the definition which says it is the reciprocal of tan .
Assuming 30 to be 30 degrees
Here θ=30
Thus it can be written in equation form as
cot 30=1tan30
Now to find the value of tan30 , we need to have the value of sin30 and cos30 as
tan θ= sin θcosθ 
Here the value of θ is 30 .
We know that the value of sin30 is 1/2 and that the value of cos30 is 32 .
So we can use this to first find the value of tan 30°
tan30=sin30/cos30=(1/2)/(3/2)=1/3
cot 30=1/tan30=1/(1/3)=3
Method 2:
We can use the formula to find the value of cot30
The formula says
cot θ=cos θ/sin θ
Here θ=30
And we know that the value of sin30 is 1/2 and that the value of cos30 is 32 .
So , by the formula
cot 30= cos30/sin30=(3/2)/(1/2)=3
Hence by both the methods , we get the same answer.

Therefore, cot30=3 is the right answer.

Note:
The value of sin is natural and changes with change in angles. It is the most common trigonometric ratio that can be used to find the value of all other trigonometric ratios. None of sine, cosine, tangent, etc. has any unit since these are all the ratios of the same quantity which is usually longer.
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