Question

How do you use a calculator to evaluate \[\cot 1.35\]?

Answer 1

Hint: The functions sine, cosine and tangent of an angle are sometimes referred to as the primary or basic trigonometric functions. Trigonometric identities are the equations involving the trigonometric functions that are true for every value of the variables involved. We know that cotangent function is the reciprocal of tangent function.

Complete step by step answer:
In most of the calculators cotangent function is not present but they do have the sine, cosine, tangent functions. We can rewrite cotangent as some combination of these functions. Since we know that cotangent function is the reciprocal of tangent function. We use this relation to solve the problem.
From the reciprocal identities of trigonometric functions. We can write cotangent function as a reciprocal of tangent function. That is
\[\Rightarrow \cot x=\dfrac{1}{\tan x}\]
On applying this identity, we can write \[\cot 1.35\] as \[\dfrac{1}{\tan 1.35}\].
\[\Rightarrow \cot 1.35=\dfrac{1}{\tan 1.35}\]
Now we can easily calculate the value of the given problem.
Firstly on the calculator and then press the number 1 and press the symbol “/”. Now press the tan button and enter the value \[1.35\]. Now press the button “Ans” to get the value.
The calculator shows the value as follows:
\[\Rightarrow \dfrac{1}{\tan 1.35}\approx 0.224\]
\[\Rightarrow \cot 1.35\approx 0.224\]
\[\therefore \] The value of \[\cot 1.35\]\[\approx 0.224\].

Note:
In order to solve such types of questions, we need to have enough knowledge over trigonometric functions and identities. We must check whether the value given is in radians or degrees. We also need to know the algebraic formulae to simplify the expressions. We must avoid calculation mistakes to get the expected answers.