Question

How do you find the \[\cot \] of a \[50\] degree angle?

Answer 1

Hint: Trigonometry tells us the relation between two sides of a right-angled triangle and one of the angles other than the right angle. Here in the given question, we have to find the value of \[\cot {50^ \circ }\] . This can be solved, by using the different ways of definition of cotangent and by using a standard calculator to get the required solution.

Complete step by step solution:
Consider
 \[ \Rightarrow \cot {50^ \circ }\]
Cotangent is one of the trigonometric ratios that is equal to the ratio of the base of the right-angled and its perpendicular, it is equal to the reciprocal of the tangent function.
 In this question, we have to find the cotangent of 50 degrees,
Now, use the definitions of cotangent ratio is:
Cotangent is defined as ratio between the cosine and sine i.e.,
 \[ \Rightarrow \cot {50^ \circ } = \dfrac{{\cos {{50}^ \circ }}}{{\sin {{50}^ \circ }}}\]
By using the calculator \[\cos {50^ \circ } = 0.6427876097\] and \[\sin {50^ \circ } = 0.7660444431\], then on substituting, we have
 \[ \Rightarrow \cot {50^ \circ } = \dfrac{{0.6427876097}}{{0.7660444431}}\]
 \[ \Rightarrow \cot {50^ \circ } = 0.8390996312 \simeq 0.8391\]
Otherwise
Cotangent is also defined as reciprocal of tangent i.e.,
 \[ \Rightarrow \cot {50^ \circ } = \dfrac{1}{{\tan {{50}^ \circ }}}\]
so it can be found by first finding the value of the \[\tan {50^ \circ }\] and then finding its reciprocal or we can find it directly.
By using the calculator \[\tan {50^ \circ } = 1.1917535926\], then
 \[ \Rightarrow \cot {50^ \circ } = \dfrac{1}{{1.1917535926}}\]
 \[ \Rightarrow \cot {50^ \circ } = 0.8390996312 \simeq 0.8391\]
Hence, the \[\cot {50^ \circ }\] is equal to \[0.8391\] .
So, the correct answer is “ \[0.8391\] ”.

Note: 50 degrees neither be expressed as a sum of two angles nor a double of an angle whose trigonometric value is known to us, that’s why we have to use the calculator. A calculator is a small electrical device that can be carried anywhere easily; it makes mathematical calculations very easy as it performs big mathematical operations in seconds. The answer obtained above is a rounded off value because we don’t require so much accuracy in our daily life works. Thus, we can find the value of unknown angles by using the knowledge of trigonometric identities but if that doesn’t work then we can find it by using a calculator.