Question

How do you evaluate $\cot 400$ ?

Answer 1

Hint:For answering this question we need to evaluate the value of $\cot 400$. From the basic concepts of trigonometry we know that the value of a complete angle is ${{360}^{\circ }}$ . So we can say that the value of any trigonometric function repeats after this value hence the value of $\cot 400$ will be $\Rightarrow \cot \left( 360+40 \right)=\cot 40$ .

Complete step by step solution:
Now considering from the question we have been asked to evaluate the value of $\cot 400$.
From the basic concepts of trigonometry we know that the value of a complete angle is ${{360}^{\circ }}$ . So we can say that the value of any trigonometric function repeats after this value hence the value of $\cot 400$ will be $\Rightarrow \cot \left( 360+40 \right)=\cot 40$ .
So we need to evaluate the value of $\cot 40$ which will give us the concluding result.
As we know that the value of $\cot 30$ is $\sqrt{3}$ and the value of $\cot 45$ is $1$ .
Therefore we can conclude that the value of $\cot 400$ will lie between the value of $\sqrt{3}$ and $1$ . If we use a calculator and evaluate its value then we will get the appropriate value as $1.1918$ .

Note: While answering questions of this type we need to have a strong knowledge of basics if we are aware of basics we can answer them easily and accurately within a short span of time. Similarly we can evaluate the value of any trigonometric function for example if we consider $\cot 405$ and try to evaluate its value then we will have the result as $\Rightarrow \cot 405=\cot \left( 360+45 \right)\Rightarrow \cot 45=1$ .