Question

How do you find the value of \[\cot 90\]?

Answer 1

Hint : Here we are given to find the value of\[\cot 90\]. To do it, first we will convert the cot function into sine and cosine function. Then we will find the value of sine and cosine functions at the angle of \[{90^\circ }\]. Then we will put those values to find the value of cot function at the angle of \[{90^\circ }\]

Complete step-by-step solution:
We are given to find the value of \[\cot 90\]. First of all we convert cot function into tan function, as below,
\[cot(\theta ) = \dfrac{1}{{tan(\theta )}}\]
Now we convert tan function into cos function and sin function as \[tan(\theta ) = \dfrac{{sin(\theta )}}{{cos(\theta )}}\]. Using this formula we move ahead as,
\[
   \Rightarrow cot(\theta ) = \dfrac{1}{{\dfrac{{sin(\theta )}}{{cos(\theta )}}}} \\
   \Rightarrow cot(\theta ) = \dfrac{{cos(\theta )}}{{sin(\theta )}} \\
 \]
Replace \[\theta \] with \[{90^\circ }\] , we get,
\[ \Rightarrow cot(90) = \dfrac{{cos(90)}}{{sin(90)}}\]
Now, since we know that the value of \[\sin 90 = 1\] and \[\cos 90 = 0\], we put these values in the above step as,
\[
   \Rightarrow cot(90) = \dfrac{0}{1} \\
   \Rightarrow \cot 90 = 0 \\
 \]
Thus we have found that the value of \[\cot 90\] is \[1\].
Formula used: We can write tan function in terms of sin and cos functions as,
\[tan(\theta ) = \dfrac{{sin(\theta )}}{{cos(\theta )}}\]
We can also write cot function in terms of tan function as
\[cot(\theta ) = \dfrac{1}{{tan(\theta )}}\]

Note: We can also find the values of different trigonometric functions for different angles by using unit circle method whose coordinates are of form,
 \[(\sin \theta ,\cos \theta )\]
Using these two trigonometric functions, we can find other trigonometric functions as well. We should also remember the values of all trigonometric functions for some of the most used angles like \[{0^\circ }, {30^\circ }, {45^\circ }, {60^\circ }, {90^\circ }\] as it will save us some time which is very crucial while solving more complex or difficult questions